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Cholesky Decomposition


Given a symmetric positive definite matrix A, the Cholesky decomposition is an upper triangular matrix U with strictly positive diagonal entries such that

 A=U^(T)U.

Cholesky decomposition is implemented in the Wolfram Language as CholeskyDecomposition[m].


See also

LU Decomposition, Matrix Decomposition, QR Decomposition

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References

Gentle, J. E. "Cholesky Factorization." §3.2.2 in Numerical Linear Algebra for Applications in Statistics. Berlin: Springer-Verlag, pp. 93-95, 1998.Nash, J. C. "The Choleski Decomposition." Ch. 7 in Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd ed. Bristol, England: Adam Hilger, pp. 84-93, 1990.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Cholesky Decomposition." §2.9 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 89-91, 1992.

Referenced on Wolfram|Alpha

Cholesky Decomposition

Cite this as:

Weisstein, Eric W. "Cholesky Decomposition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CholeskyDecomposition.html

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