ufs_ispositive, ufs_isnonnegative, ufs_type - check a quadratic form for definiteness

Calling sequence:

ufs_ispositive(M)

ufs_isnonnegative(M)

ufs_type(M)

Parameters:

M - a symmetric matrix defining a quadratic form

Synopsis:

ufs_ispositive checks whether is positive definite or not.

ufs_isnonnegative checks whether is positive semidefinite or not.

ufs_type calculates the definiteness type of . This function returns either `indefinite`, `non negative definite` or `positive definite`.

The argument must be a symmetric matrix, otherwise an error occurs.

Example:

> A:=matrix([[2,-2,0,0,1],[-2,2,0,0,-1],[0,0,2,2,0],[0,0,2,2,0],[1,-1,0,0,2]]);

> ufs_ispositive(A);

> ufs_isnonnegative(A);

> ufs_type(A);