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Eigenvalue distribution of certain ray patterns

Carolyn A. Eschenbach;  Frank J. Hall;  Zhongshan Li — 2000

Czechoslovak Mathematical Journal

In this paper, the eigenvalue distribution of complex matrices with certain ray patterns is investigated. Cyclically real ray patterns and ray patterns that are signature similar to real sign patterns are characterized, and their eigenvalue distribution is discussed. Among other results, the following classes of ray patterns are characterized: ray patterns that require eigenvalues along a fixed line in the complex plane, ray patterns that require eigenvalues symmetric about a fixed line, and ray...

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

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 matrices...

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