Similarity transformations Sample Clauses

Similarity transformations. The individual categories of ADE MFs were constructed from a finite number of indecom- posable objects up to isomorphism. We describe equivalence of MFs here by considering similarity transformations. In the context of MFs, equivalence of two MFs (E, J) and (E˜, J˜), via row and column transformations, means that there exist two invertible matri- ces S and T such that SJT −1 = J˜ , and TES−1 = E˜ . (3.31) MFs which satisfy these relations are called isomorphic. To show that the MFs after such row and column transformations are equivalent, first consider with , E, J ∈ MN (C[x]) (3.32) Q2 = W (x)I2N . (3.33) If then U = S 0 0 T , S, T ∈ MN (C[x]) , invertible (3.34) Q˜ = UQU −1 (3.35) and represents a factorisation of W (x).
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Related to Similarity transformations

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  • Creative Commons Attribution-Non-Commercial-NoDerivs License The Creative Commons Attribution Non-Commercial-NoDerivs License (CC-BY-NC-ND) permits use, distribution and reproduction in any medium, provided the original work is properly cited, is not used for commercial purposes and no modifications or adaptations are made. (see below) Use by commercial "for-profit" organizations Use of Wiley Open Access articles for commercial, promotional, or marketing purposes requires further explicit permission from Wiley and will be subject to a fee. Further details can be found on Wiley Online Library xxxx://xxxxxxx.xxxxx.xxx/WileyCDA/Section/id-410895.html Other Terms and Conditions:

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