Displaying similar documents to “The possible numbers of zeros in an orthogonal matrix.”

When does the inverse have the same sign pattern as the transpose?

Carolyn A. Eschenbach, Frank J. Hall, Deborah L. Harrell, Zhongshan Li (1999)

Czechoslovak Mathematical Journal

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By a sign pattern (matrix) we mean an array whose entries are from the set { + , - , 0 } . The sign patterns A for which every real matrix with sign pattern A has the property that its inverse has sign pattern A T are characterized. Sign patterns A for which some real matrix with sign pattern A has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal...

On zeros of regular orthogonal polynomials on the unit circle

P. García Lázaro, F. Marcellán (1993)

Annales Polonici Mathematici

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A new approach to the study of zeros of orthogonal polynomials with respect to an Hermitian and regular linear functional is presented. Some results concerning zeros of kernels are given.

A note on some characterization of invariant zeros in singular systems and algebraic criteria of nondegeneracy

Jerzy Tokarzewski (2004)

International Journal of Applied Mathematics and Computer Science

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The question how the classical definition of the Smith zeros of an LTI continuous-time singular control system can be generalized and related to state-space methods is discussed. The zeros are defined as those complex numbers for which there exists a zero direction with a nonzero state-zero direction. Such a definition allows an infinite number of zeros (then the system is called degenerate). A sufficient and necessary condition for nondegeneracy is formulated. Moreover, some characterization...

Sign patterns of J-orthogonal matrices

Frank J. Hall, Zhongshan Li, Caroline T. Parnass, Miroslav Rozložník (2017)

Special Matrices

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This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator...