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Matrices with totally signed powers

โœ Scribed by Hai-Ying Shan; Jia-Yu Shao

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
194 KB
Volume
376
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

A square real matrix A is said to have signed d-power, if the sign pattern of the power A d is uniquely determined by the sign pattern of A. A is said to have totally signed powers if A has signed d-powers for all positive integers d. A is said to be d-powerful if all the non-zero terms in the expansion formula of each entry of A d have the same sign. A is powerful if A is d-powerful for all positive integers d. We show that A has totally signed powers is equivalent to A being powerful, although A has signed d-power is not equivalent to A being d-powerful.

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