The functions in this section test matrices for positive definiteness, etc.
They may applied to any symmetric matrix over a real subring (i.e.,
Z, Q, or a real field). Each function works by calling the
function OrthogonalizeGram on its argument and then determining whether
the resulting diagonal matrix has the appropriate form.
IsPositiveDefinite(F) : ModMatRngElt -> BoolElt
Given a symmetric matrix F belonging to the matrix module S=Hom_R(M, M) or the matrix algebra S=M_n(R), where R is a subring of the real field, return whether F is positive definite, i.e., whether vFv^(tr) > 0 for all non-zero vectors v in R^n.
Given a symmetric matrix F belonging to the matrix module S=Hom_R(M, M) or the matrix algebra S=M_n(R), where R is a subring of the real field, return whether F is positive semi-definite, i.e., whether vFv^(tr) >= 0 for all non-zero vectors v in R^n.
Given a symmetric matrix F belonging to the matrix module S=Hom_R(M, M) or the matrix algebra S=M_n(R), where R is a subring of the real field, return whether F is negative definite, i.e., whether vFv^(tr) < 0 for all non-zero vectors v in R^n.
Given a symmetric matrix F belonging to the matrix module S=Hom_R(M, M) or the matrix algebra S=M_n(R), where R is a subring of the real field, return whether F is negative semi-definite, i.e., whether vFv^(tr) <= 0 for all non-zero vectors v in R^n.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]