Can the Genericity Assumption Decrease the Rank of a Matrix?
2021 ◽
Vol 65
(1)
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pp. 11-14
The genericity assumption, supposing that the nonzero parameters of a system are algebraically independent transcendentals over the field of the rationals, often helps for the mathematical modelling of linear systems. Without this condition nonzero expansion members of a determinant can cancel out each other, decreasing the rank of a matrix. In this note we show that under some circumstances an increase is also possible. This counterintuitive phenomenon is explained using some tools from matroid theory, and is illustrated by a classical network of Carlin and Youla.
2000 ◽
Vol 3
(3)
◽
pp. 249-253
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