Symbolic Math Toolbox™

svd - Symbolic singular value decomposition

Syntax

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

Description

sigma = svd(A) is a symbolic vector containing the singular values of a symbolic matrix A.

sigma = svd(vpa(A)) computes numeric singular values, using variable precision arithmetic.

[U,S,V] = svd(A) and [U,S,V] = svd(vpa(A)) return numeric unitary matrices U and V whose columns are the singular vectors and a diagonal matrix S containing the singular values. Together, they satisfy A = U*S*V'.

Symbolic singular vectors are not available.

Note   With symbolic inputs and multiple outputs, the svd function does not accept complex values as inputs.

Examples

The statements

digits(3)
A = sym(magic(4));
svd(A)
svd(vpa(A))
[U,S,V] = svd(A)

return

[         0]
[        34]
[ 2*5^(1/2)]
[ 8*5^(1/2)]

[ .311e-6*i]
[      4.47]
[      17.9]
[      34.1]
U =
 
[ -.500,  .671,  .500, -.224]
[ -.500, -.224, -.500, -.671]
[ -.500,  .224, -.500,  .671]
[ -.500, -.671,  .500,  .224]
 
 
S =
 
[     34.0,        0,        0,        0]
[        0,     17.9,        0,        0]
[        0,        0,     4.47,        0]
[        0,        0,        0, .835e-15]
 
 
V =
 
[ -.500,  .500,  .671, -.224]
[ -.500, -.500, -.224, -.671]
[ -.500, -.500,  .224,  .671]
[ -.500,  .500, -.671,  .224]

See Also

digits, eig, vpa

subs

sym