Factor a rectangular matrix into unitary and upper triangular components.
Library
Linear Algebra, in Math Functions
Description
The QR Factorization block uses modified Gram-Schmidt iteration to factor a column permutation of the M-by-N input matrix A as
where Q is an M-by-min(M,N) unitary matrix, and R is a min(M,N)-by-N upper-triangular matrix. The column-pivoted matrix Ae contains the columns of A permuted as indicated by the length-N permutation vector E.
Ae = A(:,E) % equivalent MATLAB code
Example:
The column permutation vector E is selected to ensure that the diagonal elements of matrix R are arranged in order of decreasing magnitude.
QR factorization is an important tool for solving linear systems of equations because of good error propagation properties and the invertability of unitary matrices.
Unlike LU and Cholesky factorizations, the matrix A does not need to be square for QR factorization. Note, however, that QR factorization requires twice as many operations as Gaussian elimination.
Dialog Box
- Columns in A
- The number of columns in input matrix A.
References
Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.
See Also
Cholesky Factorization
LU Factorization
QR Solver
qr (MATLAB)
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