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A completely positive matrix is a real n×n square matrix A=(a_(ij)) that can be factorized as A=BB^(T), where B^(T) stands for the transpose of B and B is any (not ...

A sequence {mu_n}_(n=0)^infty is positive definite if the moment of every nonnegative polynomial which is not identically zero is greater than zero (Widder 1941, p. 132). ...

A tensor g whose discriminant satisfies g=g_(11)g_(22)-g_(12)^2>0.

A quadratic form Q(z) is said to be positive definite if Q(z)>0 for z!=0. A real quadratic form in n variables is positive definite iff its canonical form is ...

A quantity x>0, which may be written with an explicit plus sign for emphasis, +x.

A symmetric bilinear form on a vector space V is a bilinear function Q:V×V->R (1) which satisfies Q(v,w)=Q(w,v). For example, if A is a n×n symmetric matrix, then ...

The conjugate gradient method can be viewed as a special variant of the Lanczos method for positive definite symmetric systems. The minimal residual method and symmetric LQ ...

An n×n complex matrix A is called indefinite if nonzero vectors x and y exist such that x^*Ax>0>y^*Ay, where x^* denotes the conjugate transpose. A matrix m may be tested to ...

A negative semidefinite matrix is a Hermitian matrix all of whose eigenvalues are nonpositive. A matrix m may be tested to determine if it is negative semidefinite in the ...

Any square matrix A can be written as a sum A=A_S+A_A, (1) where A_S=1/2(A+A^(T)) (2) is a symmetric matrix known as the symmetric part of A and A_A=1/2(A-A^(T)) (3) is an ...