Testing Matrix for Positive Definiteness

This helper function checks whether a given numerical matrix x is a positive-definite square matrix of a given size, without any missing values. This function is used to test if a given matrix is a covariance matrix, since every symmetric positive semi-definite matrix is a covariance matrix.

Usage

h_is_positive_definite(x, size = 2, tol = 1e-08)

Arguments

x

(matrix)
a matrix to be checked.

size

(integer)
a size of the square matrix x to be checked against for.

tol

(number)
a given tolerance number used to check whether an eigenvalue is positive or not. An eigenvalue is considered as positive if and only if it is greater than the tol.

Value

TRUE if a given matrix is a positive-definite, FALSE otherwise.

Details

The positive definiteness test implemented in this function is based on the following characterization valid for real matrices: A symmetric matrix is positive-definite if and only if all of its eigenvalues are positive. In this function an eigenvalue is considered as positive if and only if it is greater than the tol.