Cholesky Function Syntax

Cholesky Decomposition and Inverse

Description

The Cholesky Function computes the Cholesky coefficients or factors and it's Inverse from an input matrix.
The input matrix can either be defined as Symmetric, Lower Triangular or Upper Triangular.

Function Syntax

Cholesky ( Symmetric Pos. Def. Matrix to Decompose , Return Type , Activation Key )

Arguments

Input Matrix:

Excel® range containing your original matrix. The matrix must be symmetric positive definite.

Return Type:

The type of data returned by the function can be defined either as a character code or integer.

Code	Integer	Description
L, Empty cell	0	Lower Cholesky Matrix.
U	1	Upper Cholesky Matrix.
I or IL	2	Lower Cholesky Inverse.
IU	3	Upper Cholesky Inverse.

Activation Key:

Either 0 (IDLE) or 1 (ACTIVE).

The Activation key is originally due to the Automatic recalculation feature in Excel® which sends an empty matrix each time you press a key in the function wizard.

This key allows you to control the Real-Time or Snap-shot state of the function.

Return Values

The function returns a matrix or range of coefficients.
You must therefore select a range as an output field in order to display all the results.

If you have already typed the function in a single cell, you can easily expand the result by following this sequence:

Select the cell where you entered the function.
Press shift + right or down arrow, extending the cell will the arrow keys (or mouse). The formula must be in the upper left hand corner.
Once you have selected the whole range to display, hit

the F2 key {edit} and then press simultaneously on:
Shift + Ctrl + Enter.

Cholesky Validation

If you want to check returned values, multiply the output matrix by it's Transpose:

If P is a symmetric positive definite matrix C is the Cholesky decomposition of P, and C’ is the Transpose of C. You can then confirm the results by simply multiplying the resulting matrix by its transpose

P=C*C’

Further details regarding the application of Cholesky factorization are available in the application section, which you can access either through the index or See Also section.