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On The Relationship Between Conditions that Insure a PL Mapping is a Homeomorphism

M. Kojima, Romesh Saigal

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Abstract

In this note we consider two conditions which insure that a piecewise linear mapping is a homeomorphism. One of these is that the leading principal minors of certain matrices be positive, while the other is that all real eigenvalues be positive. We show that the latter condition is weaker than the former.

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In this note we consider two conditions which insure that a piecewise linear mapping is a homeomorphism. One of these is that the leading principal minors of certain matrices be positive, while the other is that all real eigenvalues be positive. We show that the latter condition is weaker than the former.

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Available abstract

In this note we consider two conditions which insure that a piecewise linear mapping is a homeomorphism. One of these is that the leading principal minors of certain matrices be positive, while the other is that all real eigenvalues be positive. We show that the latter condition is weaker than the former.

Key concepts: Homeomorphism (graph theory), Eigenvalues and eigenvectors, Mathematics, Piecewise linear function, Principal (computer security), Pure mathematics, Discrete mathematics, Mathematical analysis

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