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发帖数: 147 | 1 已知两个对称矩阵A,B，且 A－B 为半正定
A的特征值为 a_1......a_n，降序排列
B的特征值为 b_1......b_n，降序排列
那么下面的不等式是否成立
a_i>=b_i | i********e
发帖数: 31 | 2 Yes.
Matrix Analysis: Roger A. Horn, Charles R. Johnson - Google Books Result
by Roger A. Horn, Charles R. Johnson - 1985 - Science - 561 pages
"The following result, an immediate corollary of Weyl's theorem known as the
monotonicity theorem, says that all the eigenvalues of a Hermitian matrix .
.."
books.google.com/books?isbn=0521386322... |
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