Department Colloquium
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Speaker:
Skip Garibaldi Department of Mathematics Emory University, Atlanta, Georgia Time and Place: 3:30 p.m., Thursday, December 5, 2003, 411 Allen Title: The characteristic polynomial and determinant are not ad hoc constructions Abstract: How do you define the determinant of a matrix? As an alternating sum of products of entries in the matrix (like Jacobi)? Where does that magical formula come from? And what about the characteristic polynomial? Other algebraic structures, like the quaternions, also have notions of determinant and characteristic polynomial. But the definitions one sees in linear algebra don't work for those cases. In fact, the determinant and characteristic polynomial can be defined for any finite-dimensional algebra over a field (e.g., nĄżn matrices, the quaternions, a finite-degree field extension). In the case of matrices, one gets the "magical formula" as a consequence. Host: Len Miller, (662) 325-7138, miller@math.msstate.edu Refreshments: 3:00-3:30 p.m., 467 Allen |
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