On a problem of Halmos: unitary equivalence of a matrix to its transpose TeX Export

@article{citeulike:5454259, 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 naive assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix (i.e., \$T = T^t\$) holds for matrices 7x7 and smaller, but fails for matrices 8x8 and larger.}, archivePrefix = {arXiv}, author = {Garcia, Stephan R. and Tener, James E.}, citeulike-article-id = {5454259}, citeulike-linkout-0 = {http://arxiv.org/abs/0908.2107}, citeulike-linkout-1 = {http://arxiv.org/pdf/0908.2107}, day = {14}, eprint = {0908.2107}, keywords = {algebra, analysis, mathematics}, month = {Aug}, posted-at = {2009-08-18 17:07:01}, priority = {2}, title = {On a problem of Halmos: unitary equivalence of a matrix to its transpose}, url = {http://arxiv.org/abs/0908.2107}, year = {2009} }

TY - JOUR ID - citeulike:5454259 L3 - citeulike-article-id:5454259 N2 - Motivated by a problem of Halmos, we obtain a canonical decomposition for complex matrices which are unitarily equivalent to their transpose (UET). Surprisingly, the naive assertion that a matrix is UET if and only if it is unitarily equivalent to a complex symmetric matrix (i.e., $T = T^t$) holds for matrices 7x7 and smaller, but fails for matrices 8x8 and larger. TI - On a problem of Halmos: unitary equivalence of a matrix to its transpose KW - algebra KW - analysis KW - mathematics AU - Garcia, Stephan AU - Tener, James PY - 2009/Aug/14/ UR - http://arxiv.org/abs/0908.2107 ER -