# ApCoCoA-1:Num.SVD

From ApCoCoAWiki

## Num.SVD

Computes the singular value decomposition of a matrix.

### Syntax

Num.SVD(A:MAT):[U:MAT,S:MAT,VT:MAT]

### Description

*Please note:* The function(s) explained on this page is/are using the *ApCoCoAServer*. You will have to start the ApCoCoAServer in order to use it/them.

This command computes the singular value decomposition of the given matrix `A`. Let `A` be a `(m x n)` matrix. Then `A` is decomposed into the product of an orthogonal `(m x m)` matrix `U`, a transposed matrix `VT` of an orthogonal `(n x n)` matrix `V` and a real `(m x n)` matrix `S`, which contains the singular values of the matrix `A`.

@param

*A*The matrix we want to decompose.@return A list of three matrices

`[U, S, VT]`such that`A=U*S*VT`.

#### Example

D:=[[1,2,7,18],[2,4,9,12],[23,8,9,10]]; Dec(Num.SVD(D),3); -- CoCoAServer: computing Cpu Time = 0 ------------------------------- [Mat([ [<quotes>-0.473</quotes>, <quotes>-0.666</quotes>, <quotes>-0.575</quotes>], [<quotes>-0.415</quotes>, <quotes>-0.407</quotes>, <quotes>0.813</quotes>], [<quotes>-0.776</quotes>, <quotes>0.624</quotes>, <quotes>-0.084</quotes>] ]), Mat([ [<quotes>33.091</quotes>, <quotes>17.047</quotes>, <quotes>3.365</quotes>] ]), Mat([ [<quotes>-0.579</quotes>, <quotes>-0.266</quotes>, <quotes>-0.424</quotes>, <quotes>-0.642</quotes>], [<quotes>0.755</quotes>, <quotes>0.119</quotes>, <quotes>-0.159</quotes>, <quotes>-0.624</quotes>], [<quotes>-0.265</quotes>, <quotes>0.423</quotes>, <quotes>0.750</quotes>, <quotes>-0.431</quotes>], [<quotes>-0.153</quotes>, <quotes>0.857</quotes>, <quotes>-0.480</quotes>, <quotes>0.100</quotes>] ])] -------------------------------

### See also