Journal Name:
- Mathematica Æterna
Key Words:
| Author Name | University of Author |
|---|---|
Abstract (2. Language):
Let A ∈ Cn×n be normal with eigenvalues 1, . . . , n, and let t1, . . . , tn ∈ C. It is well-known that
max
∈Sn |t1(1) + · · · + tn(n)| =
max n|t1u∗1Au1 + · · · + tnu∗n
Aun| {u1, . . . , un} ⊂o Cno.
Here Sn denotes the symmetric group of order n, and ⊂o means “is an
orthonormal subset of . . . ”. If A is Hermitian and 1 ≥ · · · ≥ n, and
if t1, . . . , tn ∈ R satisfy t1 ≥ · · · ≥ tn, then
t11 + · · · + tnn =
maxnt1u∗1Au1 + · · · + tnu∗n
Aun | {u1, . . . , un} ⊂o Cno
and
tn1 + · · · + t1n =
min nt1u∗1Au1 + · · · + tnu∗n
Aun | {u1, . . . , un} ⊂o Cno.
We present bounds for the left-hand sides of all these equations by
suitable choices of u1, . . . , un.
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FULL TEXT (PDF):
- 6
329-346