`CholeskyDecomposition`¶

Returns the upper-triangular Cholesky factor U of a Hermitian positive-definite matrix such that ConjugateTranspose[U].U equals the input.

$ wo 'CholeskyDecomposition[{{4, 2}, {2, 2}}]'
{{2, 1}, {0, 1}}

Exact arithmetic keeps radicals symbolic:

$ wo 'CholeskyDecomposition[{{4, 2}, {2, 3}}]'
{{2, 1}, {0, Sqrt[2]}}

Machine-precision input yields a numeric factor:

$ wo 'CholeskyDecomposition[{{2.0, 1.0}, {1.0, 2.0}}]'
{{1.4142135623730951, 0.7071067811865475}, {0., 1.224744871391589}}

CholeskyDecomposition¶