One of the applications of LDLT-decomposition is the inversion of symmetric matrices. By its functionality, this algorithm is similar to analogous algorithms for matrices which are given by Cholesky decomposition and LU-decomposition.

Subroutine **SMatrixLDLTInverse** gets LDLT-decomposition of matrix *A* (an output of a subroutine **SMatrixLDLT**) as an input and returns matrix *A ^{ -1}* given by its lower or upper triangle depending on a variant of LDLT-decomposition (

Subroutine **SMatrixInverse** gets the lower or upper triangle of matrix A as an input, calls the subroutine **SMatrixLDLT** and inverts and returns the lower or upper triangle of matrix *A ^{ -1}*.

Both subroutines return False if the matrix is singular (in this case one of the elementary units of matrix *D* equals 0), in that case, the matrix inversion is not performed. If the matrix is not a singular and the inversion could be performed, then the subroutines return True. In that case, the matrix could be ill-conditioned, but the subroutines don't evaluate the matrix condition number.

*This algorithm is transferred from the LAPACK library.*

*This article is licensed for personal use only.*

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