Answer to: Consider a symmetric matrix A. (a) Prove that a necessary condition for A to be positive definite is that By signing up, you'll get...
摘要: Let A,B be unitary matrix(partial unitary matrix or para unitary matrix).In this paper,we give sufficient and necessary condition for A+B is unitary matrix (partial unitary matrix or para unitary matrix).Meanwhile,related expressions of A and B are also given.关键词:...
Let be a real symmetric block-matrix with A and B positive definte. Then M is positive definte if and only if. An application for this result to the stability of constant coefficient linear system is presented.关键词: Positive definite condition block-matrix linear ordinary differential equatio...
Roth in their 1978 paper "The Rigidity of Graphs" [Trans. Amer. Math. Soc., 245 (1978), pp. 279-289] and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes ...
Reid, W. T., A matrix differential equation of Riccati type. Amer. J. Math., 6, 237–246 (1948). Google Scholar John, F., Partial Differential Equations, 3rd Ed. New York: Springer-Verlag, 1978. Google Scholar Friedrichs, K. O., Symmetric hyperbolic linear differential equations. Co...
ConditionEigenvaluesMatrixPositiveSymmetricSymmetric matrix Replies: 8 Forum:Calculus and Beyond Homework Help POTWA Linear Operator with Trace Condition Let ##V## be a finite dimensional vector space over a field ##F##. If ##L## is a linear operator on ##V## such that the trace of ##L...
We study the smallest singular value of a square random matrix with i.i.d. columns drawn from an isotropic log-concave distribution. An important example is obtained by sampling vectors uniformly dis- tributed in an isotropic convex body. We deduce that the condition number of such matrices is...
It is pointed out that the coefficient matrix of any resistor-inductor-capa... KS Lu,JN Wei - 《Siam Journal on Matrix Analysis & Applications》 被引量: 59发表: 1994年 On the stable rank and reducibility in algebras of real symmetric functions Let A() denote the set of functions ...
The resulting matrix is symmetric, as it should be. View chapterExplore book Optimum Design Concepts Jasbir S. Arora, in Introduction to Optimum Design (Second Edition), 2004 4.6.5 Sufficient Conditions for Convex Programming Problems Theorem 4.11 Sufficient Condition for Convex Programming Problem If...
We consider a homogeneous differential operator and show an improved version of Murat’s condition for -quasiaffine functions, provided that the operator satisfies the constant rank condition. As a consequence, we obtain that affinity along the characteristic cone of implies -quasiaffinity if admits ...