標題: | On sums of three square-zero matrices |
作者: | Takahashi, K 應用數學系 Department of Applied Mathematics |
公開日期: | 15-二月-2000 |
摘要: | Wang and Wu characterized matrices which are sums of two square-zero matrices, and proved that every matrix with trace-zero is a sum of four square-zero matrices. Moreover, they gave necessary or sufficient conditions for a matrix to be a sum of three square-zero matrices. In particular, they proved that if an n x n matrix A is a sum of three square-zero matrices, the dim ker(A - alpha I) less than or equal to 3n/4 for any scalar alpha not equal 0. Proposition 1 shows that this condition is not necessarily sufficient for the matrix A to be a sum of three square-zero matrices, and characterizes sums of three square-zero matrices among matrices with minimal polynomials of degree 2. (C) 2000 Elsevier Science Inc, All rights reserved. |
URI: | http://hdl.handle.net/11536/30730 |
ISSN: | 0024-3795 |
期刊: | LINEAR ALGEBRA AND ITS APPLICATIONS |
Volume: | 306 |
Issue: | 1-3 |
起始頁: | 45 |
結束頁: | 57 |
顯示於類別: | 期刊論文 |