SingularValueDecomposition

SingularValueDecomposition(A)

calculates the compact Singular Value Decomposition of a matrix A. The Singular Value Decomposition of matrix A is a set of three matrices: U, S and V such that A = U × S × Transpose(V)</sup>. Let A be a m × n matrix, then U is a m × p orthogonal matrix, S is a p × p diagonal matrix with positive or null elements, V is a p × n orthogonal matrix (hence Transpose(V) is also orthogonal) where p=min(m,n).

See:

• Wikipedia - Singular value decomposition

Examples

>>> SingularValueDecomposition({{ 24/25, 43/25 },{57/25, 24/25 }})
{
{{0.6,0.7999999999999998},
 {0.7999999999999998,-0.6000000000000001}},
{{2.9999999999999996,0.0},
 {0.0,1.0}},
{{0.7999999999999998,-0.6000000000000001},
 {0.6000000000000001,0.7999999999999998}}}

Related terms

CharacteristicPolynomial, ConjugateTranspose, Det, DiagonalMatrix, Dot, Eigenvalues, Eigenvectors, HilbertMatrix, IdentityMatrix, Inverse, JacobiMatrix, LinearSolve, LUDecomposition, MatrixPower, MatrixQ, MatrixRank, NullSpace, Tr, Transpose, VandermondeMatrix, VectorQ