A reduced QR decomposition of a real 
matrix 
with 
is a matrix decomposition
of the form
 |
where 
is an 
upper triangular matrix and the columns of
the 
matrix 
form an orthonormal set,
so
 |
Here 
is the transpose of 
and 
is the identity matrix.
In a full QR decomposition, 
is an 
orthogonal matrix
and 
is 
and upper trapezoidal. For complex matrices, conjugate transpose replaces transpose,
and the full factor is a unitary matrix. A QR decomposition
can be used to solve linear systems of equations
and least squares fitting problems.
QR decomposition is implemented in the Wolfram Language as QRDecomposition[m].
