PAIRS OF MATRICES, ONE OF WHICH COMMUTES WITH THEIR COMMUTATOR
PAIRS OF MATRICES, ONE OF WHICH COMMUTES WITH THEIR COMMUTATOR
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一对矩阵，其中一个与其换向器进行换向
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发表时间：
2011
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通讯作者：
G. Bourgeois
中科院分区：
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作者：
G. Bourgeois
设A，B是n×n复矩阵，C=AB，BA，A可交换。对于n=2，我们证明了A，B是同时可三角化的。对于n�3，我们给出了矩阵A，B的一个例子，使得(A，B)对不具有Motzkin-Taussky性质，且B和C不是同时可三角化的。最后，我们估计了ALP‘in-Koreshkov检验两个矩阵是否同时可三角化的算法的复杂度。实际上，人们不能测试一对维度大于5的数值矩阵。
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 checks whether two matrices are simultaneously triangularizable. Practically, one cannot test a pair of numerical matrices of dimension greater than five.