l*******g
发帖数: 17 | 1 假设A是一已知实正定对称矩阵，特征值是 (a1,a2,...,an)
令B = DAD，其中D是任意实正定对角阵，B的特征值是(b1,b2,...,bn)
问 f(D)=max(bi)/min(bi) 的最小值是多少，或者有个bound也可以
多谢多谢！ | s**e
发帖数: 1834 | 2 Find a D such that DAD=I, so the answer is 1.
【在 l*******g 的大作中提到】
: 假设A是一已知实正定对称矩阵，特征值是 (a1,a2,...,an)
: 令B = DAD，其中D是任意实正定对角阵，B的特征值是(b1,b2,...,bn)
: 问 f(D)=max(bi)/min(bi) 的最小值是多少，或者有个bound也可以
: 多谢多谢！
| l******3
发帖数: 6 | 3 Guess your question is to solve
minimize f(D) over all D with eigenvalues equal to b1, b2,...bn.
Seems not a trivial problem.
You may try out the following method:
Let D0=diag[b1, b2,...,bn]. Your problem can then be rewritten as
minimize norm (R^T*D0*R*A*R^T*D0*R - a* Id) over all real number a,
rotation matrix R, where Id is the identity matrix and R^T is the transpose.
Then you may try to use the usual first-order condition...
The algebraic calculations are tedious but worth trying if this i |
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