Can the Genericity Assumption Decrease the Rank of a Matrix?

Autor: Recski, András, Vékássy, Áron
Předmět:
Zdroj: Periodica Polytechnica: Electrical Engineering & Computer Science; 2021, Vol. 65 Issue 1, p11-14, 4p
Abstrakt: 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. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index