STATISTICA Visual Basic Library of Matrix Functions - MatrixSingularValuesDecomp (Matrix, U, W, V)

Parameter

Description

Matrix

name of source data matrix (see Arrays in functions)

U

result matrix (see Arrays in functions)

W

vector to contain singular values computed from source matrix (see Arrays in functions)

V

result matrix (see Arrays in functions)

The MatrixSingularValuesDecomp function will perform the singular value decomposition for the specified Matrix (see also Arrays in functions). Given an input Matrix(m,n), the program will compute matrices U(m,n), W(n), V(n,n), so that Matrix = U*W-diag.*V' (where V' stands for the transposed V matrix, and W-diag. stands for a diagonal matrix(n,n), with the elements of vector W in the diagonal). If the Matrix is of reduced rank, that is, it has some columns or rows that are linear combinations of other columns or rows, then the function will return as many non-zero singular values (in vector W) as there are independent column vectors that can be constructed from the columns and rows of the singular Matrix. Thus, the number of positive singular values in vector SingularValues is equal to the rank of the source Matrix (for further discussion, see also MatrixSingularValues). Matrix U will contain a set of orthonormal vectors for each non-singular value.

Related topics. MatrixSingularValues, MatrixRank, MatrixGramSchmidtOrt. For more information on using arrays, see Arrays in functions. For a complete list of matrix functions, see STATISTICA Visual Basic library of matrix functions.