On the dimension of the algebra generated by a boolean matrix |
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| Authors: | David A Gregory Norman J Pullman Stephen J Kirkland |
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| Institution: | 1. Queen's university at Kingston , Ontario, K7L 3N6, Canada;2. University of Regina , Saskatchewan, S4S 0A2, Canada |
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| Abstract: | We investigate the subspace of the space of all n × n Boolean (0,1)-matrices, spanned by the powers of an arbitrary matrix. We estimate the maximum dimension of such spaces as a function of n and show that their bases consists of consecutive integer powers of the matrix, starting at I. We also determine the maximum dimension of the space spanned by the powers of as symmetric matrix and characterise the matrices achieving that maximum. |
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