This function returns the lower Cholesky decomposition of a square matrix fed to it. It does not check for positive semi-definiteness, although it does check for squareness. It assumes that Option Base 0 is set, and thus the matrix entry indices need to be adjusted if Base is set to 1. is called the Cholesky factor of A, and can be interpreted as a generalized square root of A, as described in Cholesky decomposition. In a 3x3 example, we have to solve the following system of equations:
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