Name
Abstract | ||
|---|---|---|
Let A=(A1, . . ., Am) be an m-tuple of n × n Hermitian matrices. For $1 \le k \le n$, the $k${\rm th} joint numerical range of A is defined by $$W_k(A) = \{ ({\rm \tr}(X^*A_1X), \dots, {\rm \tr}(X^*A_mX) ): X \in {\bf C}^{n\times k}, X^*X = I_k \}.$$ We consider linearly independent families of Hermitian matrices {A1, . . . , Am} so that Wk(A) is convex. It is shown that m can reach the upper bound 2k(n-k)+1. A key idea in our study is relating the convexity of Wk(A) to the problem of constructing rank k orthogonal projections under linear constraints determined by A. The techniques are extended to study the convexity of other generalized numerical ranges and the corresponding matrix construction problems. |
Year | DOI | Venue |
|---|---|---|
2000 | 10.1137/S0895479898343516 | SIAM Journal on Matrix Analysis and Applications |
Keywords | Field | DocType |
joint numerical range,rm th,n hermitian matrix,bf c,times k,key idea,corresponding matrix construction problem,generalized numerical range,hermitian matrix,rank k orthogonal projection,numerical range,hermitian matrices,convexity | Combinatorics,Convexity,Linear independence,Matrix (mathematics),Upper and lower bounds,Regular polygon,Numerical range,Hermitian matrix,Mathematics | Journal |
Volume | Issue | ISSN |
21 | 2 | 0895-4798 |
Citations | PageRank | References |
3 | 0.64 | 0 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chi-Kwong Li | 1 | 313 | 29.81 |
| Yiu-Tung Poon | 2 | 12 | 2.82 |