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In linear algebra, the QR decomposition of a
matrix A is a factorization expressing
A as
- A = QR
where Q is an orthogonal matrix
(QQT = I), and R is an upper triangular matrix.
The QR decomposition is often used to solve the linear least
squares problem. The QR decomposition is also the basis for a particular eigenvalue algorithm, the QR algorithm.
Actual methods to calculate the QR decomposition include Givens
rotations, Householder transformations and
the Gram-Schmidt decomposition.
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