Geometric invariant theory and the generalized eigenvalue problem
نویسندگان
چکیده
منابع مشابه
Geometric Invariant Theory and Generalized Eigenvalue Problem
Let G be a connected reductive subgroup of a complex connected reductive group Ĝ. Fix maximal tori and Borel subgroups of G and Ĝ. Consider the cone LR(G, Ĝ) generated by the pairs (ν, ν̂) of dominant characters such that Vν is a submodule of Vν̂ (with usual notation). Here we give a minimal set of inequalities describing LR(G, Ĝ) as a part of the dominant chamber. In way, we obtain results about...
متن کاملGeometric Invariant Theory and Generalized Eigenvalue Problem II
Let G be a connected reductive subgroup of a complex connected reductive group Ĝ. Fix maximal tori and Borel subgroups of G and Ĝ. Consider the cone LR◦(Ĝ,G) generated by the pairs (ν, ν̂) of strictly dominant characters such that Vν is a submodule of Vν̂ . The main result of this article is a bijective parametrisation of the faces of LR◦(Ĝ,G). We also explain when such a face is contained in ano...
متن کاملGershgorin Theory for the Generalized Eigenvalue Problem Ax — \ Bx
A generalization of Gershgorin's theorem is developed for the eigenvalue problem Ax = XBx and is applied to obtain perturbation bounds for multiple eigenvalues. The results are interpreted in terms of the chordal metric on the Riemann sphere, which is especially convenient for treating infinite eigenvalues.
متن کاملThe Definite Generalized Eigenvalue Problem: A New Perturbation Theory
Let (A, B) be a definite pair of n × n Hermitian matrices. That is, |x∗Ax| + |x∗Bx| 6= 0 for all non-zero vectors x ∈ C. It is possible to find an n × n non-singular matrix X with unit columns such that X∗(A + iB)X = diag(α1 + iβ1, . . . , αn + iβn) where αj and βj are real numbers. We call the pairs (αj, βj) normalized generalized eigenvalues of the definite pair (A, B). These pairs have not b...
متن کاملThe Eigenvalue Problem: Perturbation Theory The Unsymmetric Eigenvalue Problem
The Unsymmetric Eigenvalue Problem Just as the problem of solving a system of linear equations Ax = b can be sensitive to perturbations in the data, the problem of computing the eigenvalues of a matrix can also be sensitive to perturbations in the matrix. We will now obtain some results concerning the extent of this sensitivity. Suppose that A is obtained by perturbing a diagonal matrix D by a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2010
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-010-0233-3