Matrices with Prescribed Principal Elements and Singular Values

Canadian Mathematical Bulletin - Tập 14 Số 2 - Trang 247-249 - 1971
Graciano Neves de Oliveira1
1Instituto Gulbenkian de Ciencia, C.C.C., Oeiras, Portugal

Tóm tắt

We shall be concerned with the following problem. Let a11, …, ann be complex numbers and λ1, …, λn nonnegative real numbers. Under what conditions does there exist an n × n complex matrix A with a11, …, ann as principal elements and λ1, …, λn as singular values? This problem has been suggested in [3] but, to our knowledge, has not yet been solved.

Từ khóa


Tài liệu tham khảo

10.1112/jlms/s1-33.1.14

10.1016/0022-247X(64)90009-5

10.1090/S0002-9939-1954-0061573-6

Thompson, Principal submatrices IX: Interlacing inequalities for singular values of submatrices, Linear Algebra and its Applications (to appear)