Article - preprint
Complex symmetric matrix, Complex symmetric operator, Unitary equivalence, Unitary similarity, Unitary orbit, Transpose, Trace, Nilpotent, Truncated Toeplitz operator, UECSM, Words, SU(p, q)
A matrix T∈Mn(C) is UECSM if it is unitarily equivalent to a complex symmetric (i.e., self-transpose) matrix. We develop several techniques for studying this property in dimensions three and four. Among other things, we completely characterize 4×4 nilpotent matrices which are UECSM and we settle an open problem which has lingered in the 3×3 case. We conclude with a discussion concerning a crucial difference which makes dimension three so different from dimensions four and above.
© 2012 Elsevier B.V.
Garcia, Stephan Ramon; Poore, Daniel E. '11; and Tener, James E. '08, "Unitary Equivalence to a Complex Symmetric Matrix: Low Dimensions" (2012). Pomona Faculty Publications and Research. 242.