Chapter 4:algebraic sets,polynomials, and other functions |
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Authors: | Stephen Pierce |
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Institution: | San Diego State University , San Diego, CA, 92182 |
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Abstract: | Let T be a linear operator on the vector space V ofn×n matrices over a field F. We discuss two types of problems in this chapter. First, what can we say about T if we assume that T maps a given algebraic set such as the special linear group into itself? Second, let p(x) be a polynomial function (such as det) on V into F. What can we say about T if Tpreserves p(x), i.e. p(T(X)) = p(X) for all X in V? |
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