Unitarily achievable zero patterns and traces of words in A and A
- 作者：Dragomir Ž ; . Đ ; oković ; ; Charles R. Johnson
- 关键词：Unitary similarity ; Schur’ ; s triangularization theorem ; Specht’ ; s criterion for unitary similarity
- 刊名：Linear Algebra and its Applications
- 出版年：2007
- 期刊代码：38_00243795
- 类别：mt
- 出版时间：1 February 2007
- 卷：421
- 期：1
- 页码：63-68
- 文件大小：120 K
摘要
Our primary objective is to identify a natural and substantial problem about unitary similarity on arbitrary complex matrices: which 0-patterns may be achieved for any given n-by-n complex matrix via some unitary similarity of it. To this end, certain restrictions on “achievable” 0-patterns are mentioned, both positional and, more important, on the maximum number of achievable 0’s. Prior results fitting this general question are mentioned, as well as the “first” unresolved pattern (for 3-by-3 matrices!). In the process a recent question is answered.
A closely related additional objective is to mention the best known bound for the maximum length of words necessary for the application of Specht’s theorem about which pairs of complex matrices are unitarily similar, which seems not widely known to matrix theorists. In the process, we mention the number of words necessary for small size matrices.