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The square root function in MATLAB is sqrt(a), where a is a numerical scalar, vector or array. The square root function returns the positive square root b of each element of the argument a, such that b x b = a.Reshaped array, returned as a vector, matrix, multidimensional array, or cell array. The data type and number of elements in B are the same as the data type and number of elements in A.The elements in B preserve their columnwise ordering from A.. Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char | …If you actually look at the documentation for plot you'll see that if you pass it a matrix, it will plot each column as a separate plot object on the same axes. As such you can simply pass the transpose of your data to plot. % Example data A = magic (10); % Create a plot for each row hplot = plot (A.'); This will plot each signal using the next ...Jan 1, 2016 · M = movmean (A,[kb kf]) computes the mean with a window of length kb+kf+1 that includes the element in the current position, kb elements backward, and kf elements forward. example. M = movmean ( ___,dim) specifies the dimension of A to operate along for any of the previous syntaxes. For example, if A is a matrix, then movmean (A,k,2) …Interpolate Two Sets of 2-D Sample Values. Create a grid of 2-D sample points using ndgrid. [x,y] = ndgrid (0:10,0:5); Create two different sets of sample values at the sample points and concatenate them as pages in a 3-D array. Plot the two sets of …A Matrix is a two-dimensional array of elements. In MATLAB, the matrix is created by assigning the array elements that are delimited by spaces or commas and using semicolons to mark the end of …Write the matrix to a comma delimited text file and display the file contents. The writematrix function outputs a text file named M.txt. 17,24,1,8,15 23,5,7,14,16 4,6,13,20,22 10,12,19,21,3 11,18,25,2,9. To write the same matrix to a text file with a different delimiter character, use the 'Delimiter' name-value pair.The 2-D cross-correlation of an M -by- N matrix, X, and a P -by- Q matrix, H, is a matrix, C, of size M + P –1 by N + Q –1. Its elements are given by. C ( k, l) = ∑ m = 0 M − 1 ∑ n = 0 N − 1 X ( m, n) H ¯ ( m − k, n − l), − ( P − 1) ≤ k ≤ M − 1, − ( Q − 1) ≤ l ≤ N − 1, where the bar over H denotes complex ... Interpolate Two Sets of 2-D Sample Values. Create a grid of 2-D sample points using ndgrid. [x,y] = ndgrid (0:10,0:5); Create two different sets of sample values at the sample points and concatenate them as pages in a 3-D array. Plot the two sets of …1 Answer. Sorted by: 4. You need to use two outputs for find: [row,col] = find (A==0) The single output you got was the linear index. This is the element number by counting down the columns e.g. for your matrix these are the linear indices: 1 4 7 10 2 5 8 11 3 6 9 12. which you could also use to locate an element in a matrix (so for your ...If you have an existing 2D matrix, you can assign an element in the "3rd dimension" and the matrix is augmented to contain the new element. All other new matrix elements that have to be added to do that are set to zero. For example. B = magic(3); %# creates a 3x3 magic square B(2,1,2) = 1; %# and you have a 3x3x2 arrayA matrix is a two-dimensional array often used for linear algebra. Array Creation To create an array with four elements in a single row, separate the elements with either a comma (,) or a space. a = [1 2 3 4] a = 1×4 1 2 3 4 This type of array is a row vector. To create a matrix that has multiple rows, separate the rows with semicolons.plot (X,Y) creates a 2-D line plot of the data in Y versus the corresponding values in X. To plot a set of coordinates connected by line segments, specify X and Y as vectors of the …It is easy to find the inverse of a matrix in MATLAB. Input the matrix, then use MATLAB’s built-in inv() command to get the inverse. Open MATLAB, and put the cursor in the console window. Choose a variable name for the matrix, and type it i...Definition of Matlab 2D Array Matlab provides the functionality to implement the array, in which we can implement multidimensional arrays such as 2D arrays. With the help of a 2D array, we can manipulate the matrix, the structure of the matrix contains the rows and columns and each value from the matrix contains the row index and column index.hist (reshape (A, prod (size (A)), 1)) What it does is create a vector out of the matrix A by reshaping it into a matrix with one column and a number of rows equal to the number of elements of A: prod (size (A)) = number_of_columns (A) * number_of_rows (A) Or the short way: hist (A (:)) This takes every element of A in sequence and thus also ...Numerical gradients, returned as arrays of the same size as F.The first output FX is always the gradient along the 2nd dimension of F, going across columns.The second output FY is always the gradient along the 1st dimension of F, going across rows.For the third output FZ and the outputs that follow, the Nth output is the gradient along the Nth dimension of F.A pseudocolor plot displays matrix data as an array of colored cells (known as faces ). MATLAB ® creates this plot as a flat surface in the x - y plane. The surface is defined by a grid of x - and y -coordinates that correspond to the corners (or vertices) of the faces. The grid covers the region X=1:n and Y=1:m, where [m,n] = size (C).Feb 20, 2012 · Copy. grayImage = rgb2gray (rgbImage); Or if you have a volumetric image (like a CT or MRI image or other image distributed in 3 spatial dimensions) you can use the mean (or max or min) like this. Theme. Copy. xyImage = mean (volumeImage, 3); xzImage = mean (volumeImage, 2); yzImage = mean (volumeImage, 1); They will get you the …Create and plot 2-D data with repeated blocks. Compute the 2-D Fourier transform of the data. Shift the zero-frequency component to the center of the output, and plot the resulting 100-by-200 matrix, which is the same size as X. Pad X with zeros to compute a 128-by-256 transform. Y = fft2 (X,2^nextpow2 (100),2^nextpow2 (200)); imagesc (abs ... Creating a 784x784 matrix 10,000 times isn't going to take advantage of the vectorization in MATLAB, which is going to be more useful for small arrays. Avoiding a for loop also won't help too much, given the following: The main speedup you can gain here is by computing the inverse of the covariance matrix once, and then computing the pdf yourself.If A is vector, then flip(A) reverses the order of the elements along the length of the vector.. If A is a matrix, then flip(A) reverses the elements in each column.. If A is an N-D array, then flip(A) operates on the first dimension of A in which the size value is not 1. Smooths 2D array data. Ignores NaN's. function matrixOut = smooth2a (matrixIn,Nr,Nc) This function smooths the data in matrixIn using a mean filter over a. rectangle of size (2*Nr+1)-by- (2*Nc+1). Basically, you end up replacing. element "i" by the mean of the rectange centered on "i". Any NaN.Coding is done in MATLAB. I have looked at plot (but it only does 2D plots) and surf, which does 3D plots but doesn't work for my MxNx9 matrix of images. I have also tried to experiment with contourslice, but not sure what parameters to …I am looking for a way to pass NumPy arrays to Matlab. I've managed to do this by storing the array into an image using scipy.misc.imsave and then loading it using imread, but this of course causes the matrix to contain values between 0 and 256 instead of the 'real' values.. Taking the product of this matrix divided by 256, and the maximum …I have a 2D matrix, and I want to know the minimum and its indices. I normally use min (min (matrix)), and I found here that I can also use min (matrix (:)). But I couldn't find out how to also get the location of this found minimum? Thanks in advance! Sign in to comment. Sign in to answer this question.The creation process behind 2D animation conjures nostalgic images of smoke-filled rooms where animators labored over their slanted drafting tables, flipping between thin pages while sketching a character into life. Those days may be gone, ...Description. M = min (A) returns the minimum elements of an array. If A is a matrix, then min (A) is a row vector containing the minimum value of each column of A. If A is a multidimensional array, then min (A) operates along the first dimension of A whose size is greater than 1, treating the elements as vectors. Description. example. A = readmatrix (filename) creates an array by reading column-oriented data from a file. The readmatrix function performs automatic detection of import parameters for your file. readmatrix determines the file format from the file extension: .txt, .dat, or .csv for delimited text files.Apr 19, 2014 · 示例. plot (X,Y) 创建 Y 中数据对 X 中对应值的二维线图。. 要绘制由线段连接的一组坐标,请将 X 和 Y 指定为相同长度的向量。. 要在同一组坐标区上绘制多组坐标,请将 X 或 Y 中的至少一个指定为矩阵。. plot (X,Y,LineSpec) 使用指定的线型、标记和颜色创建绘 …A(1,4)=40 A(2,4)=100 Function has to generic for any matrix size. Please let know the function to get the above mentioned data from the matrix. Looking forward to hear from you at the earliest.Or use imshow() (if you have the Image Processing Toolbox) and apply a colormap (of which there are a wide variety of colormaps built in to MATLAB).5. If you're asking about MATLAB, the word "matrix" typically refers to a 2d array, whereas an "array" can be n-dimensional. Early versions of MATLAB supported only 2d matrices, not n-dimensional arrays. I believe support for n-dimensional arrays was introduced in version 5 of MATLAB. Share.A matrix is a two-dimensional array often used for linear algebra. Array Creation To create an array with four elements in a single row, separate the elements with either a comma (,) or a space. a = [1 2 3 4] a = 1×4 1 2 3 4 This type of array is a row vector. To create a matrix that has multiple rows, separate the rows with semicolons.MATLAB ® treats the array as a single column vector with each column appended to the bottom of the previous column. Thus, linear indexing numbers the elements in the columns from top to bottom, left to right. For example, consider a 3-by-3 matrix. You can reference the A(2,2) element with A(5), and the A(2,3) element with A(8). Create a matrix of data. Then create a heatmap of the matrix values. Use custom labels along the x-axis and y-axis by specifying the first two input arguments as the labels you want. Specify the title and axis labels by setting properties of the HeatmapChart object. i have a matrix , a= [1 2 4 6; 5 8 6 3;4 7 9 1] i want to randomly shuffle the elements of each row. how to do it?? please helpdoc filter2. doc fspecial. Yes you need two matrices. The first matrix is the data (i.e., your 100x100 matrix A) the second is your Gaussian filter h. You can make this filter with: Theme. Copy. h = fspecial ('gaussian'); y = filter2 (h, A);B = flipud(A) returns A with its rows flipped in the up-down direction (that is, about a horizontal axis).If A is a column vector, then flipud(A) returns a vector of the same length with the order of its elements reversed. If A is a row vector, then flipud(A) simply returns A.For multidimensional arrays, flipud operates on the planes formed by the first and …B = imgaussfilt (A) filters image A with a 2-D Gaussian smoothing kernel with standard deviation of 0.5, and returns the filtered image in B. example. B = imgaussfilt (A,sigma) filters image A with a 2-D Gaussian smoothing kernel with standard deviation specified by sigma. B = imgaussfilt ( ___,Name,Value) uses name-value arguments to control ...A matrix is a two-dimensional, rectangular array of data elements arranged in rows and columns. The elements can be numbers, logical values ( true or false ), dates and times, …When you use [] to automatically calculate a dimension size, the dimensions that you do explicitly specify must divide evenly into the number of elements in the input matrix, numel(A). Beyond the second dimension, the output, B, does not reflect trailing dimensions with a size of 1. For example, reshape(A,3,2,1,1) produces a 3-by-2 matrix. Multivariate Normal Distribution Overview. The multivariate normal distribution is a generalization of the univariate normal distribution to two or more variables. It is a distribution for random vectors of correlated variables, where each vector element has a univariate normal distribution.I am having trouble finding a way to remove all rows and columns that are all zeros from a 2D matrix to get a resulting 2D matrix using logical indexing. Z = [56,0,0,0,0,55; 0,0,0...Add to your 2D matrix a new column to store the total cases in each country. (Total cases in a country = active cases + recovered cases+ deaths). Also add a new row for the total active cases, recovered cases and deaths for all countries. Print with appropriate header the 2D matrix as updated (b). The data should be sorted based on the total ...Sep 18, 2023 · In MATLAB, the basic type, even for scalars, is a multidimensional array. Array assignments in MATLAB are stored as 2D arrays of double precision floating point numbers, unless you specify the number of dimensions and type. Operations on the 2D instances of these arrays are modeled on matrix operations in linear algebra.Mar 29, 2022 · It is a simple 3x3 matrix and it contains X-Y coordinates of a point. I am trying to create this matrix with "for" loop but I cannot assign 2 values (x and y) to an element. I will index the elements of the matrix for further work so I need these elements individually with their x-y coordinates. I tried the code below but I know it is not true. A(1,4)=40 A(2,4)=100 Function has to generic for any matrix size. Please let know the function to get the above mentioned data from the matrix. Looking forward to hear from you at the earliest.MATLAB ® treats the array as a single column vector with each column appended to the bottom of the previous column. Thus, linear indexing numbers the elements in the columns from top to bottom, left to right. For example, consider a 3-by-3 matrix. You can reference the A(2,2) element with A(5), and the A(2,3) element with A(8).Some MATLAB ® functions use grids in meshgrid format, while others use ndgrid format, so it is common to convert grids between the two formats. You can convert between these grid formats using pagetranspose ( as of R2020b ) or permute to swap the first two dimensions of the grid arrays. Copy. out = reshape (your_matrix,size_of_your_new_3D_maA matrix is a two-dimensional array often used for linear To transpose a matrix in MATLAB, you use the t

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1. This will not put the third dimension first as was r.

Sep 18, 2023 · In MATLAB, the basic type, even for scalars, is a multidimensional array. Array assignments in MATLAB are stored as 2D arrays of double precision floating point numbers, unless you specify the number of dimensions and type. Operations on the 2D instances of these arrays are modeled on matrix operations in linear algebra.How do you make a 2-d array in Matlab? Ask Question Asked 13 years, 7 months ago Modified 13 years, 7 months ago Viewed 54k times 4 I want to make a 2D array dij (i and j are subscripts). I want to be able to do dij = di,j-1+ (di,j-1 - di-1,dj-1)/ (4^j-1) My idea for this it to make to 1D arrays and then combine them into a 2D array.Description. example. contourf (Z) creates a filled contour plot containing the isolines of matrix Z, where Z contains height values on the x - y plane. MATLAB ® automatically selects the contour lines to display. The column and row indices of Z are the x and y coordinates in the plane, respectively. contourf (X,Y,Z) specifies the x and y ... i have an output value matrix depending on 3 inputs ranging from p10 to p11 , p20 to p21, p30 to p31. the output matrix is multidimensional depending on number of inputs. i want to write a function that gives the max value and its coordinates so to speak of the max value. matlabs max function only does 1 dimension.Jan 5, 2019 · Hello Star Strider this is exactly the concept i was looking for. I tried this and it gave me a single column vector but with reduced number of rows.If you look at the image i posted in the question the output will have equal number of rows when compared to the input.Please let me know if a modified SVD or any other similar concept is capable of …Apr 6, 2023 · To apply Binary Search first the 2D array needs to be sorted in any order that itself takes (M*N)log (M*N) time. So the total time complexity to search any element here is O ( (M * N) log (M * N)) + O (N + M) which very poor when it is compared with the time complexity of Linear Search which is just O (N*M). Therefore, Linear Search is used for ...Sep 18, 2023 · In MATLAB, the basic type, even for scalars, is a multidimensional array. Array assignments in MATLAB are stored as 2D arrays of double precision floating point numbers, unless you specify the number of dimensions and type. Operations on the 2D instances of these arrays are modeled on matrix operations in linear algebra.May 19, 2016 · Theme. Copy. z1 = squeeze (z (1, :, :)); z2 = squeeze (z (2, :, :)); the permute beforehand has the advantage you don't need to squeeze out the singleton dimension. But more importantly, there is no reason for you to split out your matrix anyway. Whenever in your later code, you use z1 you could simply use z (1, :, :) and whenever you use z2 ... Indexing into a matrix is a means of selecting a subset of elements from the matrix. MATLAB ® has several indexing styles that are not only powerful and flexible, …For example, you want to rotate 30 degrees: newmat = imrotate (mat, 30, 'crop') will rotate 30 degrees clockwise and keep the dimension same. To increase the size you can use 'full' option in imresize. To input a random value in the rotation matrix. rn = rand*90; %0-90 degrees newmat = imrotate (mat, rn, 'crop') Share.Mar 23, 2020 · matlab进行图像傅里叶变换去噪(fft2、fftshift、ifft2、ifftshift). 在数字图像处理中,去噪是一个经常进行的操作。. 除了在空域上进行去噪,比如使用均值滤波、中值滤波等等滤波器外,利用傅里叶变换在频域上进行操作也是一种非常有效的方式。. 我们知道 ...When the input argument is a string array, the double function treats each element as the representation of a floating-point value. However, when the input is a character array, double instead converts each character to a number representing its Unicode® value. As an alternative, use the str2double function.str2double is suitable when the input argument …This example shows basic techniques for creating arrays and matrices using MATLAB. Matrices and arrays are the fundamental representation of information and data in MATLAB. To create an array with multiple elements in a single row, separate the elements with either a comma ',' or a space. This type of array is called a row vector.Description. I = mat2gray (A,[amin amax]) converts the matrix A to a grayscale image I that contains values in the range 0 (black) to 1 (white). amin and amax are the values in A that correspond to 0 and 1 in I . Values less than amin are clipped to 0, and values greater than amax are clipped to 1. example. I = mat2gray (A) sets the values of ... Clone Size from Existing Array. Create an array of zeros that is the same size as an existing array. A = [1 4; 2 5; 3 6]; sz = size (A); X = zeros (sz) X = 3×2 0 0 0 0 0 0. It is a common pattern to combine the previous two lines of code into a single line: X = zeros (size (A)); A pseudocolor plot displays matrix data as an array of colored cells (known as faces ). MATLAB ® creates this plot as a flat surface in the x - y plane. The surface is defined by a grid of x - and y -coordinates that correspond to the corners (or vertices) of the faces. The grid covers the region X=1:n and Y=1:m, where [m,n] = size (C).2-D Pedestal. You can digitally filter images and other 2-D data using the filter2 function, which is closely related to the conv2 function. Create and plot a 2-D pedestal with interior height equal to one. Filter the data in A according to a filter coefficient matrix H, and return the full matrix of filtered data.Artists can render a 3D design from a 2D one with a 3D modeling program. After producing a 2D design, an artist will use the 3D modeling program's tools to project the design into 3D space. This process involves additional design decisions ...I understand that you wish to know how to compute the radial average for a 2D matrix. Please refer to the MATLAB script in the File Exchange submission link below which calculates the radial average of a 2D matrix: Radial Average. I hope this helps resolve the issue. Thanks, TusharLearn more about plot, 3d plots, multidimensional array MATLAB Hi! a = rand(10); % matrix b = repmat(a, 1, 1, 5); % makes multiple copies of your matrix in 3rd dimension I used this two lines of code to generate a 3rd dimension of my original matrix.5. If you're asking about MATLAB, the word "matrix" typically refers to a 2d array, whereas an "array" can be n-dimensional. Early versions of MATLAB supported only 2d matrices, not n-dimensional arrays. I believe support for n-dimensional arrays was introduced in version 5 of MATLAB. Share.A Matrix is a two-dimensional array of elements. InLearn more about plot, 3d plots, multidimensional array MAT

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The indices for X and Y are shifted by 1 in this formula to reflect matrix indices in MATLAB ®. Computing the 2-D Fourier transform of X is equivalent to first computing the 1-D transform of each column of X, and then taking the 1-D transform of each row of the result. In other words, the command fft2(X) is equivalent to Y = fft(fft(X).').'.[X,Y] = meshgrid(x,y) returns 2-D grid coordinates based on the coordinates contained in vectors x and y. X is a matrix where each row is a copy of x, and Y is a matrix where each column is a copy of y.The grid …In a matrix, the two dimensions are represented by rows and columns. Each element is defined by two subscripts, the row index and the column index. Multidimensional arrays are an extension of 2-D matrices and use additional subscripts for indexing. A 3-D array, for example, uses three subscripts.Compute 2-D Standard Deviation. Read a grayscale image into the workspace, then calculate the standard deviation of the pixel intensity values. I = imread ( 'liftingbody.png' ); val = std2 (I) val = 31.6897. Smoothing Involving Missing Values. Create a noisy vector containing NaN values, and smooth the data ignoring NaN values. rng (0, "twister" ) A = [NaN randn (1,48) NaN randn (1,49) NaN]; B = smoothdata (A); Smooth the data including NaN values. The average in a window containing any NaN value is NaN.The MATLAB environment uses the term matrix to indicate a variable containing real or complex numbers arranged in a two-dimensional grid. An array is, more generally, a vector, matrix, or higher dimensional grid of numbers. All arrays in MATLAB are rectangular, in the sense that the component vectors along any dimension are all the same length.The padarray function pads numeric or logical images with the value 0 and categorical images with the category <undefined>. By default, paddarray adds padding before the first element and after the last element of each dimension. B = padarray (A,padsize,padval) pads array A where padval specifies a constant value to use for padded elements or a ...Mar 13, 2009 · Smooths 2D array data. Ignores NaN's. function matrixOut = smooth2a (matrixIn,Nr,Nc) This function smooths the data in matrixIn using a mean filter over a. rectangle of size (2*Nr+1)-by- (2*Nc+1). Basically, you end up replacing. element "i" by the mean of the rectange centered on "i". Any NaN. 2-D Pedestal. You can digitally filter images and other 2-D data using the filter2 function, which is closely related to the conv2 function. Create and plot a 2-D pedestal with interior height equal to one. Filter the data in A according to a filter coefficient matrix H, and return the full matrix of filtered data.Bivariate histograms are a type of bar plot for numeric data that group the data into 2-D bins. After you create a Histogram2 object, you can modify aspects of the histogram by changing its property values. This is particularly useful for quickly modifying the properties of the bins or changing the display. Divide Scalar by Array. Create an array and divide it into a scalar. C = 5; D = magic (3); x = C./D. x = 3×3 0.6250 5.0000 0.8333 1.6667 1.0000 0.7143 1.2500 0.5556 2.5000. When you specify a scalar value to be divided by an array, the scalar value expands into an array of the same size, then element-by-element division is performed.Creating a 784x784 matrix 10,000 times isn't going to take advantage of the vectorization in MATLAB, which is going to be more useful for small arrays. Avoiding a for loop also won't help too much, given the following: The main speedup you can gain here is by computing the inverse of the covariance matrix once, and then computing the pdf yourself.Jan 1, 2018 · While MATLAB displays arrays according to their defined sizes and shapes, they are actually stored in memory as a single column of elements. A good way to visualize this concept is with a matrix. While the following array is displayed as a 3-by-3 matrix, MATLAB stores it as a single column made up of the columns of A appended one after the other. When the input argument is a string array, the double function treats each element as the representation of a floating-point value. However, when the input is a character array, double instead converts each character to a number representing its Unicode® value. As an alternative, use the str2double function.str2double is suitable when the input argument …TF = ismatrix (A) TF = logical 0. Now determine whether the array elements of A are a matrix. Check whether the second page of the 3-D array is a matrix. The syntax A (:,:,2) uses a colon in the first and second dimensions to access all rows and all columns. TF = ismatrix (A (:,:,2)) TF = logical 1.Jan 1, 2018 · While MATLAB displays arrays according to their defined sizes and shapes, they are actually stored in memory as a single column of elements. A good way to visualize this concept is with a matrix. While the following array is displayed as a 3-by-3 matrix, MATLAB stores it as a single column made up of the columns of A appended one after the other. In a matrix, the two dimensions are represented by rows and columns. Each element is defined by two subscripts, the row index and the column index. …Description. example. contourf (Z) creates a filled contour plot containing the isolines of matrix Z, where Z contains height values on the x - y plane. MATLAB ® automatically selects the contour lines to display. The column and row indices of Z are the x and y coordinates in the plane, respectively. contourf (X,Y,Z) specifies the x and y ...vq = griddata(x,y,v,xq,yq) fits a surface of the form v = f(x,y) to the scattered data in the vectors (x,y,v).The griddata function interpolates the surface at the query points specified by (xq,yq) and returns the interpolated values, vq.The surface always passes through the data points defined by x and y.Mar 29, 2022 · It is a simple 3x3 matrix and it contains X-Y coordinates of a point. I am trying to create this matrix with "for" loop but I cannot assign 2 values (x and y) to an element. I will index the elements of the matrix for further work so I need these elements individually with their x-y coordinates. I tried the code below but I know it is not true. This MATLAB function computes the mean of all values in array A. ... Average or mean of matrix elements. collapse all in page. Syntax. B = mean2(A) Description. example.Regarding the code I posted above, it turns out to be faster to use a 2D gpuAarray instead of a 3D gpuArray in place of the cell. This allows for a very straighforward selection of the columns and vectorization of the farthest inside loop. More precisely: % generate test data: K = 4000; M = 2; A_cell = cell (1,M); % this is given externally s ...Normalize data in a vector and matrix by computing the z -score. Create a vector v and compute the z -score, normalizing the data to have mean 0 and standard deviation 1. v = 1:5; N = normalize (v) N = 1×5 -1.2649 -0.6325 0 0.6325 1.2649. Create a matrix B and compute the z -score for each column. 27 thg 12, 2019 ... ... 2D Array Output-2D Arr