QR decomposition of matrix.
Syntax: @qr(M, R[, P])
M: matrix
R: matrix
P: (optional) matrix
Return: matrix
Decomposes an
matrix
into an
orthogonal matrix
and an
upper triangular matrix
such that
, where
.
If permutation matrix
is provided, the decomposition produces
and
such that
.
Examples
matrix m1 = @mnrnd(7, 5)
matrix r
matrix q = @qr(m1, r)
generates a random matrix M1, then decomposes it into the orthogonal matrix Q, and the upper triangular matrix R.
The following illustrate the properties of the decomposition:
sym i1 = @inner(q)
matrix m2 = q * r
where I1 is the identity matrix, and M2 is equal to M1.
Cross-references