Cholesky decomposition of a matrix
square, positive definite matrix
Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[LUDecomposition], instead.
- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.
The routine cholesky computes the cholesky decomposition of the matrix A.
The result is a lower triangular matrix R such that R⁢transpose⁡R=A.
This decomposition assumes the matrix A is positive-definite. I.e. R exists with real elements on the diagonal. cholesky will fail with an error when called on a demonstrably non-positive-definite matrix.
The command with(linalg,cholesky) allows the use of the abbreviated form of this command.
S ≔ matrix⁡3,3,1,2,3,0,1,1,0,0,4
S ≔ 123011004
A ≔ evalm⁡transpose⁡S &* S
A ≔ 1232573726
R ≔ cholesky⁡A
R ≔ 100210314
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