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Equivalence and Similarity
Applied Math| Speaker: | Paul Fuhrmann, Ben Gurion University |
| Location: | 693 Kerr |
| Start time: | Tue, Oct 12 2004, 4:10PM |
Two finite dimensional linear transformations $A$ and $B$ are similar if and only if there exists an invertible linear transformation for which $B = RAR^{-1}$. Equivalently, if and only if there exists an invertible linear transformation for which $RA=BR$. It is well known that similarity holds if and only if the linear pencils $zI-A$ and $zI-B$ are equivalent. The distinction between the two formulations is the starting point for the analysis of functional models, module structures and module homomorphisms as well as their invertibility properties. We look at special cases in various contexts, algebraic and analytic. Some connections to the analysis of linear systems will be pointed out.