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Matrices 485
QR QR Factorization. Factorizes an m×n matrix A numerically
as Q*R, where Q is an orthogonal matrix and R is an
upper triangular matrix, and returns R. R is stored in var2
and Q=A*inv(R) is stored in var1.
QR(matrix A,var1,var2)
Example:
QR returns
SCHUR Schur Decomposition. Factorizes a square matrix into two
matrices. If matrix is real, then the result is
{[[orthogonal]],[[upper-quasi triangular]]}.
If matrix is complex, then the result is
{[[unitary]],[[upper-triangular]]}.
SCHUR(matrix)
Example:
SCHUR returns
SVD Singular Value Decomposition. Factorizes an m × n matrix
into two matrices and a vector:
{[[m × m square orthogonal]],[[n × n square orthogonal]],
[real]}.
SVD(matrix)
Example:
SVD returns
12
34
0.3612 0.9486
0.9486 0.3162–
3.1622 4.4271
0 0.6324
10
01
,,
12
34
0.4159 0.9093
0.9093 0.4159
5.3722 1
5.55
17–
10 0.3722–
,
12
34
0.4045 0.9145–
0.9145 0.4045
5.4649 0.3659
0.5760 0.8174
0.8174 0.5760–
,,