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Knowledge Base

Calculates the Cholesky lower triangular factorization or decomposition. For a given matrix A, chol returns a lower triangular matrix L such that A is the matrix product of L and its conjugate transpose. The matrix A can be real or complex but it must be Hermitian and positive-definite. 

 

Supported Product: FDTD, MODE, DEVICE, INTERCONNECT

 

Syntax

Description

L = chol(A);

Returns a lower triangular matrix L that satisfies the equation A = mult(L,ctranspose(L))

 

Example

Find the Cholesky decomposition of a 3x3 matrix.

?A = [4, 12, -16; 12, 37, -43; -16,-43,98];

?L = chol(A);

?mult(L,ctranspose(L)); #This should be the same as A

result: 

4  12  -16  

12  37  -43  

-16  -43  98  

result: 

2+0i  0+0i  0+0i  

6+0i  1+0i  0+0i  

-8+0i  5+0i  3+0i  

result: 

4+0i  12+0i  -16+0i  

12+0i  37+0i  -43+0i  

-16+0i  -43+0i  98+0i  

 

See Also

Functions, mult, ctranspose

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