Algebra 819-Homework 2

Abstract

1 Let K be a field, V a finite-dimensional vector space over K, and T ∈ EndK(V ). For k ∈ K and S ∈ EndK(V ), define kS : V → V, v → k S(v). (a) Let Φ : K[x] → EndK(V ) be defined by Φ(k0 + k1x + k2x + . . . + knx) = k0T 0 + k1T 1 + k2T 2 + . . . + knT, where T 0 = idV . This is well-defined because a polynomial is completely determined by its coefficients… (More)

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