SingularValueDecomposition

SingularValueDecomposition(matrix)

calculates the singular value decomposition for the matrix.

SingularValueDecomposition returns u, s, w such that matrix =u s v, u' u=1, v' v=1, and s is diagonal.

See:

• Wikipedia: Singular value decomposition

Examples

>> SingularValueDecomposition({{1.5, 2.0}, {2.5, 3.0}})
{
{{0.5389535334972082,0.8423354965397538},
 {0.8423354965397537,-0.5389535334972083}},
{{4.635554529660638,0.0},
 {0.0,0.10786196059193007}},
{{0.6286775450376476,-0.7776660879615599},
 {0.7776660879615599,0.6286775450376476}}}

Symbolic SVD is not implemented, performing numerically.

>> SingularValueDecomposition({{3/2, 2}, {5/2, 3}})
{
{{0.5389535334972082,0.8423354965397538},
 {0.8423354965397537,-0.5389535334972083}},
{{4.635554529660638,0.0},
 {0.0,0.10786196059193007}},
{{0.6286775450376476,-0.7776660879615599},
 {0.7776660879615599,0.6286775450376476}}}

Argument {1, {2}} at position 1 is not a non-empty rectangular matrix.

>> SingularValueDecomposition({1, {2}})
SingularValueDecomposition({1, {2}})

Implementation status

• ✅ - full supported

Github

• Implementation of SingularValueDecomposition