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- W1984002574 abstract "We present a simple characterization of the maximum possible rank of the product of several real matrices, when certain entries of the matrices are constrained to be zero. Our result relates this ‘generic rank’ to the maximum number of independent ‘information paths’ through the matrices, and has as corollaries, besides several previous attempts at this problem, a new characterization of structurally fixed modes for linear time-invariant dynamical systems. Furthermore, our characterization translates immediately to an O(n5/2) algorithm for calculating the generic rank (and therefore detecting fixed modes), by solving a network flow problem (here n is the sum of the dimensions of the matrices)." @default.
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- W1984002574 date "1984-09-01" @default.
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- W1984002574 title "A simple criterion for structurally fixed modes" @default.
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- W1984002574 doi "https://doi.org/10.1016/s0167-6911(84)80074-2" @default.
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