# ApCoCoA-1:Num.SVD

## 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>]
])]
-------------------------------
```