Further results on controllability and the linear equation Ax = b |
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| Authors: | J LOUISELL E B LEE |
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| Affiliation: | Department of Electrical Engineering and Department of Mathematics , University of Minnesota , Minneapolis, U.S.A |
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| Abstract: | The linear equation Ax = b, with A an n × n matrix and b an n × l matrix over a unique factorization domain R, is related to the controllability submodule U of the pair (A, b). It is shown that the above equation has a solution lying in V if, and only if, A is unimodular as an operator on U. An example is given of a matrix which is unimodular as an operator on the controllability submodule, but not as an operator on Rn and sparseness of this occurrence is discussed. |
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