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