TTMC25. m-Isometries and Their Properties
Speaker: Dr. Trieu Le (Lê Long Triều), The University of Toledo, USA
Title: m-Isometries and Their Properties
Abstract: Isometries are linear transformations that preserve lengths. The identity matrix gives rise to an isometry and so does any diagonal matrix whose entries on the diagonal have absolute value one. On the other hand, any nontrivial Jordan block having all 1's on the diagonal is not an isometry but it satisfies a matrix equation whose coefficients are the same as those in the binomial expansion of (1-t)^m for a certain value of m. Such matrices are called m-isometries. In this talk, I shall provide several examples of m-isometries and discuss their interesting properties.