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Some questions remain staggered matrix space

Author: SunWei
Tutor: CaoZhongGuang
School: Heilongjiang University
Course: Basic mathematics
Keywords: alternate matrix real antisymmetric matrix preserving antitripotence endomorphism matrix max-rank determinant
CLC: O151.21
Type: Master's thesis
Year: 2011
Downloads: 11
Quote: 0
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Abstract


Suppose R is a field of real numbers and F is a field with chF = 2. Let n≥4be an integer, K_n (R) and K_n (F) denote the set of all n×n antisymmetric matricesover R and the set of n×n alternate matrices over F, respectively. Denote byωK_n (F) the subset of K_n (F) consisting of all max-rank matrices. If A3 = ?A,A∈Rn×n, A is called an antitripotence matrix. A matrix A∈K_n (F) is saidto have max-rank if rank(A) = n (resp., n ? 1 ) when n is even(resp.,odd). Anadditive mapφ: K_n (F)→K_n (F) is said to preserve the max-rank ifφ(ωK_n (F)) =ωK_n (F). An additive mapφ: K_n (F)→K_n (F) is said to preserve the determinantif detφA = detA. In chapter 2, this paper characterizes linear operators preservingantitripotence on K_n (R) by using the result about the linear rank-2 preserverson K_n (F); In chapter 3, we describe the additive max-rank preservers on K_n (F)by using the result about the additive rank-2 preservers on K_n (F). Furthermore,we, applying the result about additive preservers of the max-rank, characterize theadditive preservers of the determinant on K_n (F).

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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