Cholesky decomposition of a real symmetric positive-definite matrix

For a real symmetric positive-definite matrix, A, the Cholesky decomposition, A=LL^T (where L is lower-triangular), is more efficient than the LU-decomposition. Read the book and/or Wikipedia article Cholesky-decomposition.

Implement Cholesky decomposition of a real symmetric positive-definite matrix using Cholesky-Banachiewicz or Cholesky-Crout algorithms.

Try implement also the corresponding linear equation solver, calculation of determinant, and calculation of the inverse matrix.