ILNumerics - Technical Computing Tools

High Performance Framework for Visualization

and Computing in Industry and Science

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# The Cholesky Decomposition in .NET (C#, Visual Basic)

With the cholesky decomposition a symmetric real or hermitian complex matrix $A$ is factorized into a lower triangular matrix $L$. It is necessary that the matrix $A$ is positive definite.

$$A = L \cdot L^*$$

where $^*$ indicates the transpose and complex conjugate.

## Using the Cholesky Decomposition in .NET (C#, Visual Basic)

If the matrix A is not positive definite L will contain a submatrix that is lower triangular.