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QccMatrixNullspace - generate orthonormal basis for nullspace of
matrix
#include "libQccPack.h"
int QccMatrixNullspace(const
QccMatrix matrix1, int num_rows, i num_cols, QccMatrix matrix2, int *num_cols2);
QccMatrixNullspace() creates an orthonormal basis for the
nullspace of matrix1 which is a matrix of size num_rows x num_cols. This
orthonormal basis is returned as the columns of matrix2; that is, the
columns of matrix2 span the space that is orthogonal to the space spanned
by the columns of matrix1. matrix2 must be allocated to be of size num_cols
x num_cols prior to calling QccMatrixNullspace() (Note: this is not num_rows
x num_cols!)
The number of basis vectors in the orthogonal nullspace basis
is returned as num_cols2; num_cols2 will be less than num_cols. matrix2
will contain num_cols - num_cols2 columns of zeros. If matrix1 is of full
rank, num_cols2 will be zero, and matrix2 will be all zero.
QccMatrixNullspace()
is implemented via a call to QccMatrixSVD(3)
to generate the singular
value decomposition of matrix1. Then, the right singular vectors corresponding
to zero singular values, if any, are returned in matrix2.
QccMatrixSVD(3)
,
QccMatrix(3)
, QccPack(3)
Copyright (C) 1997-2021 James E. Fowler
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