# ApCoCoA-1:Num.SVD

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## 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([
["-0.473", "-0.666", "-0.575"],
["-0.415", "-0.407", "0.813"],
["-0.776", "0.624", "-0.084"]
]), Mat([
["33.091", "17.047", "3.365"]
]), Mat([
["-0.579", "-0.266", "-0.424", "-0.642"],
["0.755", "0.119", "-0.159", "-0.624"],
["-0.265", "0.423", "0.750", "-0.431"],
["-0.153", "0.857", "-0.480", "0.100"]
])]
-------------------------------
```