# ApCoCoA-1:Num.SVD

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This article is about a function from ApCoCoA-1. |

## 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"] ])] -------------------------------

### See also