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.
Arguments
- x
(
matrix
)
a matrix to be checked.- size
(
integer
)
a size of the square matrixx
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 thetol
.
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
.