Related papers: Grassman semialgebras and the Cayley-Hamilton theo…
Using the natural notion of {\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, "{\em each endomorphism…
The purpose of this short note is to consider multi-variate Hasse-Schmidt derivations on exterior algebras and to show how they easily provide remarkable identities, holding in the algebra of square matrices, which generalise the classical…
The Cayley--Hamilton--Newton theorem for half-quantum matrices is proven.
We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…
We establish the analogue of the Cayley--Hamilton theorem for the quantum matrix algebras of the symplectic type.
The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.
Let $A$ be a semisimple Banach algebra with non-trivial, and possibly infinite-dimensional socle. Addressing a problem raised by Harte and Hernandez, we first define a characteristic polynomial for elements belonging to the socle, and we…
The aim of this paper is to prove a Cayley-Hamilton-Ziebur Theorem for non-autonomous semilinear matrix differential equations. Moreover, we show the applicability of results like these to ODE theory.
We use the exterior product of double forms to reformulate celebrated classical results of linear algebra about matrices and bilinear forms namely the Cayley-Hamilton theorem, Laplace expansion of the determinant, Newton identities and…
We prove that the m-generated Grassmann algebra can be embedded into a 2^{m-1}x2^{m-1} matrix algebra over a factor of a commutative polynomial algebra in m indeterminates. Cayley-Hamilton and standard identities for nxn matrices over the…
In this note, we use the concept of a polynomial ring to give an elementary proof to Cayley-Hamilton Theorem. We also give an elementary proof to Birkhoff theorem on Bi-stochastic matrices.
We give a physical derivation of generalized Kahler geometry. Starting from a supersymmetric nonlinear sigma model, we rederive and explain the results of Gualtieri regarding the equivalence between generalized Kahler geometry and the…
The deep interconnection between linear algebra and graph theory allows one to interpret classical matrix invariants through combinatorial structures. To each square matrix A over a commutative ring K, one can associate a weighted directed…
We give a uniform proof of a significant part of the Cachazo-Douglas-Seiberg-Witten conjecture by using topology and geometry of infinite Grassmannians.
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
This paper is a continuation of [arXiv:1603.02204]. Exploded layered tropical (ELT) algebra is an extension of tropical algebra with a structure of layers. These layers allow us to use classical algebraic results in order to easily prove…
We develop the general Theory of Cayley Hamilton algebras using norms and compare with the approach, valid only in characteristic 0, using traces and presented in a previous paper $T$-ideals of Cayley Hamilton algebras, 2020,…
In this note, the first-order Dickson polynomials are introduced through a particular case of the expression of the trace of the $n^{th}$ power of a matrix in terms of powers of the trace and determinant of the matrix itself. The technique…
Algebraic dichotomy is a generalization of an exponential dichotomy (Lin, JDE2009). This paper gives a version of Hartman-Grobman linearization theorem assuming that linear system admits an algebraic dichotomy, which generalizes the…
The q-generalizations of the two fundamental statements of matrix algebra -- the Cayley-Hamilton theorem and the Newton relations -- to the cases of quantum matrix algebras of an "RTT-" and of a "Reflection equation" types have been…