| Synopsis
| R := Cholesky(A) computes the Cholesky decomposition of the
matrix A.
A is the input matrix, and must be a square, symmetric, positive
definite matrix.
If A does not satisfy these conditions, an error is returned.
R is a square matrix, lower triangular, such that R*transpose(R) = A.
Cholesky is used to check for positive-definiteness, and at the same time
it allows to solve a system Ax=b (by doing two back-substitutions) if it
is positive-definite. |
| Examples
| > A := [[3,1,2],[1,2,-1],[2,-1,5]];
A := [[3, 1, 2], [1, 2, -1], [2, -1, 5]]
> R := Cholesky(A);
R := [[1.7321, 0, 0], [0.5774, 1.2910, 0], [1.1547, -1.2910, 1.4142]]
> R * R^t;
[[3.0000, 1, 2], [1, 2, -1.0000], [2, -1.0000, 5.0000]]
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