How to do SVD in R

This recipe helps you do SVD in R

Recipe Objective

How to do SVD in R.

The singular value decomposition is an important statistical technique. SVD — singular value decomposition is a technique that decomposes a single matrix into 3 matrices. SVD = **mat = UDV^T** where, mat - is an m x n matrix. U — m x n orthogonal matrix / left singular vectors D — n x n diagonal matrix / Singular values V — n x n orthogonal matrix (transposed) / right singular vectors. In R, single value decomposition of a matrix can be found using svd () function. This recipe demonstrates an example of SVD.

Step 1 - Define a matrix

mat <- matrix(c(1:8), nrow = 4, ncol = 4, byrow = TRUE) print(mat)

"matrix is" :
     [,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    5    6    7    8
[3,]    1    2    3    4
[4,]    5    6    7    8

Step 2 - Calculate the SVD

SVD = svd(mat) print(SV)

"Output of code ":
$d
[1] 2.012059e+01 1.778133e+00 1.816415e-16 1.097509e-16

$u
           [,1]       [,2]       [,3]       [,4]
[1,] -0.2659911  0.6551708 -0.1573275 -0.6893824
[2,] -0.6551708 -0.2659911 -0.6893824  0.1573275
[3,] -0.2659911  0.6551708  0.1573275  0.6893824
[4,] -0.6551708 -0.2659911  0.6893824 -0.1573275

$v
           [,1]       [,2]       [,3]       [,4]
[1,] -0.3520617 -0.7589813 -0.5452993  0.0514657
[2,] -0.4436258 -0.3212416  0.6887054 -0.4750630
[3,] -0.5351899  0.1164981  0.2584870  0.7957289
[4,] -0.6267540  0.5542377 -0.4018931 -0.3721316

d - returns the singualr value vectors of the matrix u - left singular matrix v - right singular matrix

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