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 ...
A necessary and sufficient condition for the positive-definiteness of interval symmetric matrices is obtained, and a useful application is shown. SHI, ZHI-CHENG,GAO, WEI-BIN - 《International Journal of Control》 被引量: 95发表: 1986年 Comments on 'a necessary and sufficient condition for the ...
Least singular value and condition number of a square random matrix with i.i.d. rows We consider a square random matrix made by i.i.d. rows with any distribution and prove that, for any given dimension, the probability for the least singular value to be in [0; $\\epsilon$) is at ...
The well-known absolute bound condition for a primitive symmetric association scheme ( X , S ) gives an upper bound for | X | in terms of | S | and the minimal non-principal multiplicity of the scheme. In this paper we prove another upper bounds for | X | for an arbitrary primitive...
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...
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...
A unified simple condition for stable matrix,positive definite matrix and M matrix is presented in this paper.Based on the established conditon,a simplified method which is easy to use for judging those matrices is proposed.Three illustrative examples are given to show the applications of the prop...
Unitary equivalence to a complex symmetric matrix: An algorithm We present a necessary and sufficient condition for a 3 × 3 matrix to be unitarily equivalent to a symmetric matrix with complex entries, and an algorithm... James,E.,Tener - 《Journal of Mathematical Analysis & Applications》 被...
What is the necessary condition for matrix commutation? Hi all! I was wondering what the necessary condition is for two arbitrary matrices, say A and B, to commute: AB = BA. I know of several sufficient conditions (e.g. that A, B be diagonal, that they are symmetric and their product...
Existing definitions of backward error and condition number for linear systems do not cater for structure in the coefficient matrix, except possibly for sparsity. We extend the definitions so that when the coefficient matrix has structure the perturbed matrix has this structure too. We show that whe...