QR decomposition

15.3.2 QR decomposition

The QR decomposition of a square matrix A is A=QR, where Q is an orthogonal matrix (Q^TQ=I) and R is upper triangular. The qr command finds the QR decomposition of a matrix.

qr takes A, a numeric square matrix.
qr(A) returns a list [Q,R] with Q and R from the QR decomposition.

Examples

A:=[[3,5],[4,5]]:; qr(A)

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

−

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

⎡
⎢
⎣

5	7
0	1

⎤
⎥
⎦

qr([[1,2],[3,4]])

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

√

−

√

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦

⎡
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣

√

⎤
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎦