Document Type
Article - preprint
Department
Mathematics (Pomona)
Publication Date
2012
Keywords
Complex symmetric matrix, Complex symmetric operator, Unitary equivalence, Unitary similarity, Unitary orbit, Transpose, Trace, Nilpotent, Truncated Toeplitz operator, UECSM, Words, SU(p, q)
Abstract
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.
Rights Information
© 2012 Elsevier B.V.
Terms of Use & License Information
DOI
10.1016/j.laa.2012.01.029
Recommended Citation
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.
https://scholarship.claremont.edu/pomona_fac_pub/242
Comments
Pre-print from http://arxiv.org/abs/1104.4960
Final publication can be found at:
Stephan Ramon Garcia, Daniel E. Poore, James E. Tener, Unitary equivalence to a complex symmetric matrix: Low dimensions, Linear Algebra and its Applications, Volume 437, Issue 1, 1 July 2012, Pages 271-284, ISSN 0024-3795, http://dx.doi.org/10.1016/j.laa.2012.01.029. (http://www.sciencedirect.com/science/article/pii/S0024379512000936)