On a problem of Halmos: Unitary equivalence of a matrix to its transpose

12/02/2011 - 1:30pm
12/02/2011 - 2:30pm
Speaker: 
Stephan Garcia
Abstract: 

Halmos asked whether every square complex matrix is unitarily equivalent to its transpose (UET). Ad hoc examples indicate that the answer is no. In this talk, we give a complete characterization of matrices which are UET. Surprisingly, the naive conjecture that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix is true in dimensions n ≤ 7 but false for n ≥ 8. In particular, unexpected building blocks begin to appear in dimensions 6 and 8. This is joint work with James E. Tener (UC Berkeley).

Where: 
Millikan 213, Pomona College
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