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Calculus and Beyond Homework Help
Find monic generators of the ideals
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[QUOTE="andrewkirk, post: 6007641, member: 265790"] I don't know what they mean by ##S(\epsilon_j;W)## but usually problems about matrices and monic generators of ideals are concerned with the [URL='https://en.wikipedia.org/wiki/Minimal_polynomial_(linear_algebra)']minimal polynomial of a matrix[/URL], and the ideals in question are ideals of the polynomial ring ##F[x]##, which will be a principal ideal domain, so that any ideal of it can be generated by a single monic polynomial. The minimal polynomial of a matrix A is the unique monic polynomial that can generate the ideal consisting of all polynomials ##p[x]## in ##F[x]## such that ##f[A]=0##. Here 'monic' means that the highest-order coefficient of the polynomial is 1. You might find [URL='https://math.stackexchange.com/questions/766145/find-the-monic-generator-of-and-ideal']this stackexchange problem[/URL] helpful. [/QUOTE]
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Find monic generators of the ideals
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