Tropical compound matrix identities
نویسندگان
چکیده
منابع مشابه
Identities via Bell matrix and Fibonacci matrix
In this paper, we study the relations between the Bell matrix and the Fibonacci matrix, which provide a unified approach to some lower triangular matrices, such as the Stirling matrices of both kinds, the Lah matrix, and the generalized Pascal matrix. To make the results more general, the discussion is also extended to the generalized Fibonacci numbers and the corresponding matrix. Moreover, ba...
متن کاملGeneralized compound matrix method
In this work we demonstrate how the extension of the Evans function method using the compound matrix approach can be implemented to undertake the stability analysis (normally done through numerical means) of nonlinear travelling waves. The main advantage of this approach is that it can easily overcome the stiffness which is normally associated with these kinds of problems. We present a general ...
متن کاملThe Tropical Rank of a Tropical Matrix
In this paper we further develop the theory of matrices over the extended tropical semiring. Introducing a notion of tropical linear dependence allows for a natural definition of matrix rank in a sense that coincides with the notions of tropical regularity and invertibility.
متن کاملTropical Arithmetic and Tropical Matrix Algebra
This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial, notions of regularity and invertibility arise naturally for matrices over this semiring; we show that a tropical matrix is invertible if and only if it is r...
متن کاملWitnessing Matrix Identities and Proof Complexity
We use results from the theory of algebras with polynomial identities (PI algebras) to study the witness complexity of matrix identities. A matrix identity of d× d matrices over a field F is a non-commutative polynomial f(x1, . . . , xn) over F, such that f vanishes on every d×d matrix assignment to its variables. For any field F of characteristic 0, any d > 2 and any finite basis of d× d matri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2018
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.04.006