Related papers: A simple proof of Jordan normal form
We classify decompositions of simple special finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic zero into the sum of two proper simple subsuperalgebras.
In this note, we prove that any Jordan derivation on the generalized matrix ring $T_n(R,M)$ is a derivation. This extends some well-known results of this branch due to Bre\v{s}ar et al. in the cited literature.
We determine the Newton trees of the rational polynomials of simple type, thus filling a gap in the proof of the classification of these polynomials given by Neumann and Norbury.
We give a canonical form of m-by-2-by-2 spatial matrices for equivalence over any field.
This is a note of purely didactical purpose as the proof of the Jordan measure decomposition is often omitted in the related literature. Elementary proofs are provided for the existence, the uniqueness, and the minimality property of the…
This paper presents a formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar subdivisions, formal specifications and proofs assisted by the Coq system. Fundamental properties are proven by…
Let $V$ be a finite dimensional vector space over a field $\mathrm{k}$ of characteristic $0$. Let $A$ be a linear mapping of $V$ into itself. This paper gives a normal form for $A$, which gives a better description of the structure of $A$…
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…
In this paper we prove the following result. Let $G$ be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field $F$ of characteristic $p\geq 0$, and let $u\in G$ be a nonidentity unipotent…
Jordan isomorphisms of rings are defined by two equations. The first one is the equation of additivity while the second one concerns multiplicativity with respect to the so-called Jordan product. In this paper we present results showing…
We compute the exact values of the Jordan constants of abelian surfaces over finite fields.
We classify simple finite Jordan conformal superalgebras and establish preliminary results for the classification of simple finite Jordan pseudoalgebras.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
Normal and composition series of groups enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is proved.
A new elementary nonstandard proof of the Jordan curve theorem is given. The proof (the technical part consists of 4 pages) is self-contained, except for the Jordan theorem for polygons taken for granted.
We present matrix identities which yield respectively the Jordan canonical form of the Pascal matrix P_n = (i -1 choose j -1)_{1 <= i,j <= n} modulo a prime, the eigenvectors of (i choose j)_{1 <= i,j <= n}, and the Smith normal form of…
This note contains a short proof of a classical result: any rational symplectic matrix can be put in diagonal form after right and left multiplication by integral symplectic matrices.
Normal and composition series of modules enumerated by ordinal numbers are studied. The Jordan-Holder theorem for them is discussed.
The aim of this note is to show that the "usual" proof of the Maschke Theorem in the case of a real and complex field can not be generalized at least to the case of a field of rational functions on a non-singular curve.
The purpose of this note is to advertise an elegant algorithmic proof for the Jordan--Chevalley decomposition of a matrix, following and (slightly) revising the discussion of Couty, Esterle und Zarouf (2011). The basic idea of that method…