Saturday, 9 May 2020

Matrix Utilities: Cholesky Decomposition for Real Matrix

This blog post implements the Cholesky decomposition of a square matrix, as well as matrix inversion based on forward and backward substitution on the decomposition matrices. For a Cholesky decomposition to be feasible, the matrix must be positive definite and Hermitian. As the calculator here deals with matrices with only real number entries, the matrix will thus need to be symmetric (as well as positive definite).

For the (square) matrix entry, comma separated (the separation can also be a single whitespace) numbers need to be entered into the Input box, with no newline after the last line. A comma at the end of each line can be added optionally for comma separated numbers. Alternatively, you can load a CSV file into the Input box, by clicking on the Choose File button.

The precision of the results in decimal places can be specified in the text box headed "Precision (decimal places)". To perform the calculation, simply press the button labelled "Perform Cholesky decomposition" further down this page. The resulting Cholesky matrices displayed (in the pink boxes) will be the lower and upper triangular matrices. Finally, the matrix inverse will be displayed in the yellow box.

Precision (decimal places)


Results pending...

Cholesky Matrix: Lower Triangular

Cholesky Matrix: Upper Triangular

Matrix Inverse