Unitary Equivalence of a Matrix to Its Transpose

Authors

Stephan Ramon Garcia, Pomona CollegeFollow
James E. Tener '08, Pomona College

Student Co-author

Pomona Undergraduate

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2012

Keywords

unitarily equivalent to its transpose, complex symmetric matrix

Abstract

Motivated by a problem of Halmos, we obtain a canonical decomposition for complex matrices which are unitarily equivalent to their transpose (UET). Surprisingly, the na\"ive assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix holds for matrices $7 \times 7$ and smaller, but fails for matrices $8 \times 8$ and larger.

Rights Information

© 2012 Theta Foundation

Terms of Use & License Information

Terms of Use for work posted in Scholarship@Claremont.

Recommended Citation

Garcia, S.R., Tener, J.E., Unitary equivalence of a matrix to its transpose, J. Operator Theory 68 (2012), no. 1, 179-203. MR2966041