Authors
Eurice de Souza, SP Bhattacharyya
Publication date
1981/8/1
Journal
Linear Algebra and its Applications
Volume
39
Pages
167-188
Publisher
North-Holland
Description
A closed-form finite series representation of the unique solution X of the matrix equation AX − XB=C is developed. Using this representation, the image, kernel, and rank of X are related to the controllable and unobservable subspaces of the (A, C) and (C, B) pairs respectively. Bounds on the rank of X are obtainedin terms of the dimensions of these subspaces. In the case that C has unitary rank, an exact calculation of rank X is made. The generic rank of X with A, B fixed and C generic is evaluated.
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Scholar articles
E de Souza, SP Bhattacharyya - Linear Algebra and its Applications, 1981