![]() "Matrix differential calculus with applications in the multivariate linear model and its diagnostics". ^ Liu, Shuangzhe Leiva, Victor Zhuang, Dan Ma, Tiefeng Figueroa-Zúñiga, Jorge I.Matrix differential calculus with applications in statistics and econometrics. ^ Magnus, Jan Neudecker, Heinz (2019).Hands-on Matrix Algebra Using R: Active and Motivated Learning with Applications. "Simultaneous Reduction and Vec Stacking". "The R package 'sn': The Skew-Normal and Related Distributions such as the Skew-t". "Typing Linear Algebra: A Biproduct-oriented Approach". It is also used in local sensitivity and statistical diagnostics. Vectorization is used in matrix calculus and its applications in establishing e.g., moments of random vectors and matrices, asymptotics, as well as Jacobian and Hessian matrices. In R, function vec() of package 'ks' allows vectorization and function vech() implemented in both packages 'ks' and 'sn' allows half-vectorization. In Python NumPy arrays implement the flatten method, while in R the desired effect can be achieved via the c() or as.vector() functions. ![]() GNU Octave also allows vectorization and half-vectorization with vec(A) and vech(A) respectively. Using the elements from A, create a 2-by-2-by-3 multidimensional array. As long as the number of elements in each shape are the same, you can reshape them into an array with any number of dimensions. For example, reshape a 3-by-4 matrix to a 2-by-6 matrix. prod then multiples the elements of each column to return the result. M prod ( reshape (V,3, ) ) M 3exp (x), 18x, 49, 24x2, 4xsin (x) reshape calculates that five columns are required for a matrix of three rows. In Matlab/ GNU Octave a matrix A can be vectorized by A(:). The reshape function changes the size and shape of an array. This lets reshape automatically calculate the number of columns required for three rows. Programming languages that implement matrices may have easy means for vectorization. There exist unique matrices transforming the half-vectorization of a matrix to its vectorization and vice versa called, respectively, the duplication matrix and the elimination matrix.
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