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.

• @param A The matrix we want to decompose.

• @return This function returns a list of three matrices which form the singular value decomposition of the input matrix. The list produced is [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([
  [<quote>-0.473</quote>, <quote>-0.666</quote>, <quote>-0.575</quote>],
  [<quote>-0.415</quote>, <quote>-0.407</quote>, <quote>0.813</quote>],
  [<quote>-0.776</quote>, <quote>0.624</quote>, <quote>-0.084</quote>]
]), Mat([
  [<quote>33.091</quote>, <quote>17.047</quote>, <quote>3.365</quote>]
]), Mat([
  [<quote>-0.579</quote>, <quote>-0.266</quote>, <quote>-0.424</quote>, <quote>-0.642</quote>],
  [<quote>0.755</quote>, <quote>0.119</quote>, <quote>-0.159</quote>, <quote>-0.624</quote>],
  [<quote>-0.265</quote>, <quote>0.423</quote>, <quote>0.750</quote>, <quote>-0.431</quote>],
  [<quote>-0.153</quote>, <quote>0.857</quote>, <quote>-0.480</quote>, <quote>0.100</quote>]
])]
-------------------------------

See also

Introduction to CoCoAServer

Num.QR

Num.EigenValues

Num.EigenValuesAndVectors

Num.EigenValuesAndAllVectors