cholesky decomposition in matlab

In MATLAB, you can use the chol function to compute the Cholesky decomposition of a positive definite matrix. The Cholesky decomposition factorizes a positive definite matrix into the product of a lower triangular matrix and its conjugate transpose.

Here is the general syntax to compute the Cholesky decomposition in MATLAB:

main.m
L = chol(A)
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where A is the positive definite matrix and L is the lower triangular matrix.

Here's a simple example:

main.m
A = [4, 12, -16; 12, 37, -43; -16, -43, 98];
L = chol(A)
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The output L will be:

main.m
L = 2   0   0
    6   1   0
   -8   5   3
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You can verify that L is the lower triangular matrix by checking that all the elements above the main diagonal are zero.

Note that the chol function will return an error if the input matrix is not positive definite. So make sure your matrix A is positive definite before applying the Cholesky decomposition.

I hope this helps!