WOLFRAM|DEMONSTRATIONS PROJECT

QR Decomposition

​
size of matrix
3
maximum entry abs value
3.13
random seed
integer entries
A
Q
R
​
​
​
​
2.5
1.1
0.3
2.2
1.9
0.4
1.8
0.1
0.3
=
-0.7
0.1
-0.7
-0.6
-0.7
0.4
-0.5
0.7
0.5
-3.8
-1.9
-0.6
0.
-1.1
0.
0.
0.
0.1
The QR decomposition of a square matrix A factors A as the product of an orthogonal matrix Q and an upper triangular matrix R. An orthogonal matrix is a matrix whose columns are mutually orthogonal unit vectors and so satisfies
T
Q
Q=I
, where
I
is an identity matrix, and an upper triangular matrix is a matrix whose entries below the main diagonal are all zero. The matrix Q is the result of performing the Gram-Schmidt process on the columns of A. The Mathematica function QRDecomposition[a] accomplishes this factorization, producing the list

T
Q
,R
.