The nonnegative definiteness of a symmetric partitioned matrix can be characterized in an interesting way in terms of submatrices. Our experience is that this characterization is a very handy tool in various problems related to the Löwner partial ordering....
M. Hlad´ik. Positive semidefiniteness and positive definiteness of a linear parametric interval matrix. to appear in a Springer book series, 2016.Hlad´ik, M.: Positive semidefiniteness and positive definiteness of a linear para- metric interval matrix (2018)...
Define definiteness. definiteness synonyms, definiteness pronunciation, definiteness translation, English dictionary definition of definiteness. adj. 1. a. Clearly defined; explicitly precise: a definite statement of the terms of the will. See Synonyms a
Specially, we show that the smallest real eigenvalue of M-tensor is positive corresponding to a nonnegative eigenvector. We propose an algorithm to find the smallest positive eigenvalue and then apply the property to study the positive definiteness of a multivariate form....
Theorem 16.4To determine the definiteness-of a quadratic form (13) of n variables,Q(x)=x′Ax. when restricted to a constraint set (14) given by m linear equationsBx=0. construct the(n+m)×(n+m)symmetric matrixHby bordering the matrixAabove and to the left by the coefficientsBof the...
摘要: It is shown how the Schur complement theory can be used for the derivation of criteria for the definiteness (or semidefiniteness) of the restriction of a quadratic form to the null space of a matrix.关键词: CiteSeerX citations and Crouzeix J.-P Definiteness and semidefiniteness of ...
We show that strong observability is equivalent to the definiteness of a corresponding quadratic functional, and particularly to a certain asymptotic behaviour of solutions of associated Riccati matrix differential equations. The main tools for the proofs are an application of Ehrling's lemma and a ...
For a full tensor, an M -matrix with diagonal dominance can be obtained subject to a sufficient condition for ellipticity. Positive definiteness of the ... MG Edwards,CF Rogers - 《Computational Geosciences》 被引...
Related to #148, from a performance point of view it would be preferable to default to false for a sum of LMs as well in my view. Here is a MWE that is fairly close to actual use cases. using LinearMaps using BenchmarkTools using SparseA...
Sylvester Criterion for Positive Definiteness