Some sign patterns that allow a real inverse pair B and B−1

Sign Patterns That Allow a Positive or Nonnegative Left Inverse

An m by n sign pattern S is an m by n matrix with entries in {+,−, 0}. Such a sign pattern allows a positive (resp., nonnegative) left inverse, provided that there exist an m by n matrix A with the sign pattern S and an n by m matrix B with only positive (resp., nonnegative) entries satisfying BA = In, where In is the n by n identity matrix. For m > n ≥ 2, a characterization of m by n sign patt...

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Sign patterns that allow eventual positivity

Several necessary or sufficient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n ≥ 2, the minimum number of positive entries in an n×n sign pattern that allows eventual positivity is n+1, and to classify all 2×2 and 3×3 sign patterns a...

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Ela Sign Patterns That Allow Eventual Positivity

Several necessary or sufficient conditions for a sign pattern to allow eventual positivity are established. It is also shown that certain families of sign patterns do not allow eventual positivity. These results are applied to show that for n ≥ 2, the minimum number of positive entries in an n×n sign pattern that allows eventual positivity is n+1, and to classify all 2×2 and 3×3 sign patterns a...

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Sign Patterns That Require or Allow

A matrix A is power-positive if some positive integer power of A is entrywise positive. A sign pattern A is shown to require power-positivity if and only if either A or −A is nonnegative and has a primitive digraph, or equivalently, either A or −A requires eventual positivity. A sign pattern A is shown to be potentially power-positive if and only if A or −A is potentially eventually positive.

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Ela Sign Patterns That Require or Allow Power - Positivity

A matrix A is power-positive if some positive integer power of A is entrywise positive. A sign pattern A is shown to require power-positivity if and only if either A or −A is nonnegative and has a primitive digraph, or equivalently, either A or −A requires eventual positivity. A sign pattern A is shown to be potentially power-positive if and only if A or −A is potentially eventually positive. 1...

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Some sign patterns that allow a real inverse pair B and B−1

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منابع مشابه

Sign Patterns That Allow a Positive or Nonnegative Left Inverse

Sign patterns that allow eventual positivity

Ela Sign Patterns That Allow Eventual Positivity

Sign Patterns That Require or Allow

Ela Sign Patterns That Require or Allow Power - Positivity

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