# svd

Singular value decomposition.

## Syntax

S = svd(A)

[U,S,V] = svd(A)

[U,S,V] = svd(A,econ)

## Inputs

`A`- The matrix to decompose.
`econ`- Economy decomposition flag. Set to 0.

## Outputs

- U
- Matrix of left singular vectors.
- S
- Singular value diagonal matrix.
- V
- Matrix of right singular vectors.

## Example

Economy svd example.

`[U,S,V] = svd([1,2,3;4,5,6;7,8,10;11,12,15],0)`

```
U = [Matrix] 4 x 3
-0.12878 0.91972 0.34283
-0.31141 0.23912 -0.87513
-0.51828 0.08294 -0.06716
-0.78602 -0.30011 0.33482
S = [Matrix] 3 x 3
28.15923 0.00000 0.00000
0.00000 0.99730 0.00000
0.00000 0.00000 0.25179
V = [Matrix] 3 x 3
-0.48469 -0.84674 0.21934
-0.54664 0.09748 -0.83167
-0.68283 0.52301 0.51011
```

## Comments

[U,S,V] = svd(A) computes matrices U, S and V such that A = U*S*V'. For the economy decomposition of an mxn matrix A with m>n, U is mxn, with both S and V being nxn.

svd uses the LAPACK routines 'dgesvd' for real matrices and 'zgesvd' for complex matrices.