Cholesky decomposition of a symmetric, positive definite real square matrix.  The matrix is decomposed as the product of lower and upper triangular matrices, written as either UT∙U or L∙LT.

Syntax

T = Csky(M, Type)

Argument

Name

Description

M

A symmetric positive definite square matrix of real values.

Type

A string, either ‘upper’ (default) or ‘lower’.  Indicates whether to return the upper or lower triangular matrix.

Output

Name

Description

T

The Cholesky decomposition triangular factor.

Example

Find the Cholesky decomposition of a symmetric positive definite matrix.

Syntax

M = [40,2,3;2,40,4;3,4,40];// Given matrix

l = Csky(M, ‘lower’);

Result

l = 6.3246      0        0

   0.31623     6.3166   0

   0.47434     0.6095   6.2772

Comments

Cholesky decomposition is used for solving linear equations Ax = b. If A is symmetric and positive definite, then you can solve Ax = b by first computing the Cholesky decomposition A = LLT, then solving Ly = b for y, and finally solving LTx = y for x.

The procedure with the UTU notation is the same.

See Also:

LU

svd