QR Decomposition
Given a Matrix A, its QR-decomposition is of the form
where
is an upper Triangular Matrix and 
is an Orthogonal Matrix, i.e., one satisfying
where I is the Identity Matrix. This matrix decomposition can be used to solve linear systems of equations.See also Cholesky Decomposition, LU Decomposition, Singular Value Decomposition
References
Householder, A. S. The Numerical Treatment of a Single Non-Linear Equations. New York: McGraw-Hill, 1970. Nash, J. C. Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd ed. Bristol, England: Adam Hilger, pp. 26-28, 1990. Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``QR Decomposition.'' §2.10 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 91-95, 1992. Stewart, G. W. ``A Parallel Implementation of the QR Algorithm.'' Parallel Comput. 5, 187-196, 1987. ftp://thales.cs.umd.edu/pub/reports/piqra.ps.
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