# Cholesky Factorization

This module illustrates Cholesky factorization of a symmetric positive
definite matrix. This factorization expresses the initial matrix
*A* as a product of a lower triangular matrix and its
transpose, *A* =
*L**L*^{T}.
Because the matrix is symmetric, the algorithm accesses only the lower
triangular portion. Each successive column is divided by the square
root of its diagonal entry, and then a multiple of the scaled column is
subtracted from each remaining column.

The user first selects a matrix size (*n* = 2, 3, or
4), then selects a matrix by choosing a preset example, a random
matrix, or typing in desired entries. Since the matrix is symmetric,
only its lower triangle is shown in the computational display. The
successive steps of Cholesky factorization are carried out sequentially
by repeatedly clicking on NEXT or on the currently highlighted step.
The current column is indicated by an arrow. When Cholesky
factorization is complete, the resulting lower triangular Cholesky
factor is shown. Formats provided for displaying numeric entries
include exponential (e), fixed (f), and generic (g), with g the
default.

**Reference:** Michael T. Heath,
*Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 2.5.1, especially Algorithm 2.7 and Example 2.21.

**Developers:** Jessica Schoen and Michael Heath