Displaying similar documents to “Positivity with Respect to the Round Cone”

On quadratic Hurwitz forms. I

Jiří Gregor (1981)

Aplikace matematiky

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Homogeneous quadratic polynomials f in n complex variables are investigated and various necessary and sufficient conditions are given for f to be nonzero in the set Γ ( n ) = z ∈ C ( n ) : R e z > 0 . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.

On the computation of the minimal polynomial of a polynomial matrix

Nicholas Karampetakis, Panagiotis Tzekis (2005)

International Journal of Applied Mathematics and Computer Science

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The main contribution of this work is to provide two algorithms for the computation of the minimal polynomial of univariate polynomial matrices. The first algorithm is based on the solution of linear matrix equations while the second one employs DFT techniques. The whole theory is illustrated with examples.

Matrix quadratic equations column/row reduced factorizations and an inertia theorem for matrix polynomials

Irina Karelin, Leonid Lerer (2001)

International Journal of Applied Mathematics and Computer Science

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It is shown that a certain Bezout operator provides a bijective correspondence between the solutions of the matrix quadratic equation and factorizatons of a certain matrix polynomial (which is a specification of a Popov-type function) into a product of row and column reduced polynomials. Special attention is paid to the symmetric case, i.e. to the Algebraic Riccati Equation. In particular, it is shown that extremal solutions of such equations correspond to spectral factorizations of...