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.

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