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GivensElim

Function GivensElim


Calling Sequence  GivensElim(A)
Parameters
NameTypeDescription

A an m x n numerical matrix 
Return Type  [matrix, matrix] ([Q,R])
Synopsis GivensElim factors an m x n matrix A into two factors, A = Q*R. This decomposition is done with individual Givens' rotations. The decomposition is commonly called the QR-decomposition. Q is an m x m square orthonormal matrix, that is Q*Q^t = I. R is an m x n upper triangular matrix. If the matrix is found to be singular, then R will have zeros in the diagonal and the decomposition is still correctly done.
References Computermathematik, Walter Gander, Birkhauser, Ch 5.3
Examples
> GivensElim( [[1,2], [-2,3]] );
[[[-0.4472, -0.8944], [0.8944, -0.4472]], [[-2.2361, 1.7889], [0, -3.1305]]]
See also Cholesky,   convolve,   Eigenvalues,   GaussElim,   Identity,   matrix,   matrix_inverse,   transpose