相关论文: Limit and extended limit sets of matrices in Jorda…
In this note, a simple proof Jordan normal form and rational form of matrices over a field is given.
The dimensions of sets of matrices of various types, with specified eigenvalue multiplicities, are determined. The dimensions of the sets of matrices with given Jordan form and with given singular value multiplicities are also found. Each…
We give a self contained and elementary description of normal forms for symplectic matrices, based on geometrical considerations. The normal forms in question are expressed in terms of elementary Jordan matrices and integers with values in…
We consider perturbations of a large Jordan matrix, either random and small in norm or of small rank. In both cases we show that most of the eigenvalues of the perturbed matrix are very close to a circle with centre at the origin. In the…
We obtain general upper bounds of the sizes and the numbers of Jordan blocks for the eigenvalues $\lambda \not= 1$ in the monodromies at infinity of polynomial maps.
There exists a generalization of the concept, completely bounded norm for multilinear maps on C*-algebras. We will use the word, Jordan norm, for this norm. The Jordan norm of a multilinear map is obtained via factorizations of the map,…
We introduce a natural notion of determinant in matrix JB$^*$-algebras, i.e., for hermitian matrices of biquaternions and for hermitian $3\times 3$ matrices of complex octonions. We establish several properties of these determinants which…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
The question of matrix similarity is a classical one in linear algebra. For a field $\mathbb{F}$ and some positive integer $n \in \mathbb{N}$, one may consider the following problems: 1. Given two matrices $A, B \in \mathrm{GL}(n,…
We study the monodromies and the limit mixed Hodge structures of families of complete intersection varieties over a punctured disk in the complex plane. For this purpose, we express their motivic nearby fibers in terms of the geometric data…
Given only the dimension, $n$, of a square matrix $A \in M(n,\mathbb{C})$, how many Segre Characteristic equivalent matrices are there? Jordan Normal Form Theorem states that any linear operator over $\mathbb{C}$ is similar to a matrix in…
Triangular matrix rings are example of trivial extensions. In this article we describe the Jordan superderivations of the trivial extensions and upper triangular matrix rings. We deduce then that any Jordan superderivation of an upper…
In this paper, we classify Jordan superalgebras of dimension up to three over an algebraically closed field of characteristic different of two. Our main motivation to obtain such classification comes out from the intention to give an answer…
Linear upper bounds may be derived by imposing specific structural conditions on a generating set, such as additional constraints on ranks, eigenvalues, or the degree of the minimal polynomial of the generating matrices. This paper…
We completely characterize the higher rank numerical range of the matrices of the form $J_n(\alpha)\oplus\beta I_m$, where $J_n(\alpha)$ is the $n\times n$ Jordan block with eigenvalue $\alpha$. Our characterization allows us to obtain…
We explore Jordan derivations of triangular matrices with entries from an additively idempotent semiring. The main result states that for any matrix A over additively idempotent semiring, if we put all the elements of the family of dense…
The aim of this article is to start a study of Jordan derivations in finite endomorphism semirings.
We formulate a lattice theoretical Jordan normal form theorem for certain nilpotent lattice maps satisfying the so called JNB conditions. As an application of the general results, we obtain a transparent Jordan normal base of a nilpotent…
We study the set $\partition{\nb}$ of all possible Jordan canonical forms of nilpotent matrices commuting with a given nilpotent matrix $B$. We describe $\partition{\nb}$ in the special case when $B$ has only one Jordan block. In the…
We consider limits over categories of extensions and show how certain well-known functors on the category of groups turn out as such limits. We also discuss higher (or derived) limits over categories of extensions.