The invariant factors of a module over a principal ideal domain (PID) occur in one form of the structure theorem for finitely generated modules over a principal ideal domain. If is a PID and a finitely generated -module, then for some integer and a (possibly empty) list of nonzero elements for which . The nonnegative integer is called the free rank or Betti number of the module , while are the invariant factors of and are unique up to associatedness. The invariant factors of a matrix over a PID occur in the Smith normal form and provide a means of computing the structure of a module from a set of generators and relations. (Wikipedia).
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👉 Learn how to factor polynomials using the sum or difference of two cubes. A polynomial is an expression of the form ax^n + bx^(n-1) + . . . + k, where a, b, and k are constants and the exponents are positive integers. To factor an algebraic expression means to break it up into expression
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From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
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From playlist Mathematics
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From playlist Lie Groups and Lie Algebras
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Lecture 6, Systems Represented by Differential Equations | MIT RES.6.007 Signals and Systems
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I was on a bit of a roll today but although I did the first three questions very quickly, it wasn't 100% satisfying because for the first one I couldn't see what it had to do with invariants, and for the second and third I relied on happening to have the right piece of knowledge, though th
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From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
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