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

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

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).

Millikan 213, Pomona College
Analysis Seminar-Garcia.pdf40.49 KB