منابع مشابه
Pairs of Matrices with Property L(0
1. It was proved by Frobenius [l] that any function f(A, B) of two commutative «X« square matrices A, B has as characteristic roots the numbers /(X¿, Hi) where X¿ are the characteristic roots of A and pi the characteristic roots of B, both taken in a special ordering independent of the function /. However, commutativity of A and B is known not to be a necessary condition [2]. Matrices which hav...
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Let A, B be n × n complex matrices such that C = AB − BA and A commute. For n = 2, we prove that A, B are simultaneously triangularizable. For n ≥ 3, we give an example of matrices A, B such that the pair (A, B) does not have property L of Motzkin-Taussky, and such that B and C are not simultaneously triangularizable. Finally, we estimate the complexity of the Alp’in-Koreshkov’s algorithm that ...
متن کاملControllability of pairs of matrices with prescribed entries
Let F be an infinite field and let (A1, A2) = [ a1,1 a1,2 a2,1 a2,2 ] , [ a1,3 a2,3 ] , where the entries ai,j ∈ F , i ∈ {1, 2}, j ∈ {1, 2, 3}. In this paper we establish necessary and sufficient conditions under which it is possible to prescribe some entries of A1 A2 , so that the pair (A1, A2) is completely controllable. © 2011 Elsevier Ltd. All rights reserved.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1952
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1952-0049855-8