首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到10条相似文献,搜索用时 109 毫秒
1.
In this paper we classify linear maps preserving commutativity in both directions on the space N(F) of strictly upper triangular (n+1)×(n+1) matrices over a field F. We show that for n3 a linear map on N(F) preserves commutativity in both directions if and only if =+f where is a product of standard maps on N(F) and f is a linear map of N(F) into its center.  相似文献   

2.
3.
In this note, we show that the set of all commuting d-tuples of commuting n×n matrices that are contained in an n-dimensional commutative algebra is a closed set, and therefore, Gerstenhaber's theorem on commuting pairs of matrices is a consequence of the irreduciblity of the variety of commuting pairs. We show that the variety of commuting triples of 4×4 matrices is irreducible. We also study the variety of n-dimensional commutative subalgebras of Mn(F), and show that it is irreducible of dimension n2n for n4, but reducible, of dimension greater than n2n for n7.  相似文献   

4.
Let A, B denote the companion matrices of the polynomials xm,xn over a field F of prime order p and let λ,μ be non-zero elements of an extension field K of F. The Jordan form of the tensor product (λI + A)⊗(μI + B) of invertible Jordan matrices over K is determined via an equivalent study of the nilpotent tranformation S of m × n matrices X over F where(X)S = A TX + XB. Using module-theoretic concepts a Jordan basis for S is specified recursively in terms of the representations of m and n in the scale of p, and reduction formulae for the elementary divisors of S are established.  相似文献   

5.
Let T be a linear operator on the space of all m×n matrices over any field. we prove that if T maps rank-2 matrices to rank-2 matrices then there exist nonsingular matrices U and V such that either T(X)=UXV for all matrices X, or m=n and T(X)=UXtV for all matrices X where Xt denotes the transpose of X.  相似文献   

6.
Let Vdenote either the space of n×n hermitian matrices or the space of n×nreal symmetric matrices, Given nonnegative integers r,s,t such that r+S+t=n, let G( r,s,r) denote the set of all matrices in V with inertia (r,s,t). We consider here linear operators on V which map G(r,s,t) into itself.  相似文献   

7.
It is shown that if W is a linear subspace of real n × n matrices, such that rank (A) = k for all 0 ≠ AW, then dim Wn. If dim W = n.5≤ n is prime, and 2 is primitive modulo n then k =1.  相似文献   

8.
Let F be an algebraically closed field. We denote by i(A) the number of invariant polynomials of a square matrix A, which are different from 1. For A,B any n×n matrices over F, we calculate the maximum of i(XAX-1+B), where X runs over the set of all non-singular n×n matrices over F.  相似文献   

9.
In this note we prove that there is no linear mapping T on the space of n-square symmetric matrices over any subfield of real field such that the determinant of A is equal to the permanent of T(A) for all symmetric matrices A if n≥3.  相似文献   

10.
Consider the n-square matrices over an infiniie field Kas an n2-dimcnsional vector space M( nK). We determine all linear maps Ton M(nK) such that discriminant TX- discriminant Xfor all Xin M(nK)  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号