Generalization of Gracia's Results
Keyword(s):
Let α be a linear transformation of the m à n-dimensional vector space M_{mÃn}(C) over the complex field C such that α(X) = AX âXB, where A and B are mÃm and nÃn complex matrices, respectively. In this paper, the dimension formulas for the kernels of the linear transformations α^2 and α^3 are given, which generalizes the work of Gracia in [J.M. Gracia. Dimension of the solution spaces of the matrix equations [A, [A, X]] = 0 and [A[A, [A, X]]] = 0. Linear and Multilinear Algebra, 9:195â200, 1980.].
1969 ◽
Vol 21
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pp. 414-417
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2004 ◽
Vol 134
(3)
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pp. 477-499
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1985 ◽
Vol 28
(3)
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pp. 319-331
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1993 ◽
Vol 45
(2)
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pp. 357-368
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