Q-R decomposition with positive diagonals of R Matrix

Q-R decomposition with positive diagonals for a square random matrix
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Updated 24 Feb 2015

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In linear algebra, a QR decomposition (also called a QR factorization) of a matrix is a decomposition of a matrix A into a product A = QR of an orthogonal matrix Q and an upper triangular matrix R. QR decomposition is often used to solve the linear least squares problem, and is the basis for a particular eigen value algorithm, the QR algorithm. If A has n linearly independent columns, then the first n columns of Q form an orthonormal basis for the column space of A. More specifically, the first k columns of Q form an orthonormal basis for the span of the first k columns of A for any 1 ≤ k ≤ n. The fact that any column k of A only depends on the first k columns of Q is responsible for the triangular form of R.

Cite As

Gnaneswar Nadh satapathi (2024). Q-R decomposition with positive diagonals of R Matrix (https://www.mathworks.com/matlabcentral/fileexchange/49807-q-r-decomposition-with-positive-diagonals-of-r-matrix), MATLAB Central File Exchange. Retrieved .

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Version Published Release Notes
1.2.0.0

Q-R decomposition for random matrix with positive diagonal elements

1.1.0.0

Positive diagonals of R matrix for a random input matrix

1.0.0.0