This eigenvalue problem has a generalization to majorized sums of Hermitian matrices, due to S. Friedland. We further illustrate the common features between these two eigenvalue problems and their connection to Schubert calculus of Grassmannians. Our main result gives a Schubert calculus ...
Eigenvalues of sums of Hermitian matrices 来自 ResearchGate 喜欢 0 阅读量: 91 作者: A Horn 摘要: Let a=(a19, an) and β=(β19, βn) be arbitrary nonincreasing sequences of real numbers. We consider the question: for which nonincreasing sequences 7=(yl9, 7) do there exist ...
This is a personally satisfying paper for me, as it connects the work I did as a graduate student (with Allen Knutson and Chris Woodward) on sums of Hermitian matrices, with more recent work I did (with Van Vu) on random matrix theory, as well as several other results by other authors...
The saturation theorem of Knutson and Tao concerns the nonvanishing of Littlewood-Richardson coefficients. In combination with work of Klyachko, it implies Horn's conjecture about eigenvalues of sums of Hermitian matrices. This eigenvalue problem has a generalization to majorized sums of Hermitian matr...
The superscript on AH stands for Hermitian transpose and denotes the complex conjugate transpose of a complex matrix. If the matrix is real, then AT denotes the same matrix. In Matlab, these transposed matrices are denoted by A'. The term "eigenvalue" is a partial translation of the German...
CONVEX AND CONCAVE FUNCTIONS OF SINGULAR VALUES OF MATRIX SUMS This question comes from the proof of theorem 11 linked above. Assume A,B,C=A+BA,B,C=A+B are n×nn×n Hermitian positive semidefinite matrices with eigenvalues α1⩾α2⩾⋯⩾αn,β1⩾β2⩾...
Degeneracy of the eigenvalues of hermitian matrices is analyzed in terms of algebraic relations between the matrix elements. Only finite-dimensional matrices are considered, representing Hamiltonians of spin systems in particular.The analysis is in terms of linear relations in the space of 'diagonal' ...
Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate three by three Hermitian matrices is given, and the structure of ...
We study the asymptotic distribution of singular values and eigenvalues of non-Hermitian block Toeplitz matrices, generated by a matrix-valued periodic function f , supposed to be L 2 . A distribution result concerning singular values, due to Avram, Parter and Tyrtyshnikov, is extended to the ...
In our case, we use a family of such matrices, where instead of we use certain powers of a parameter . This result seems to be of independent interest. 2 Bounds for bipartite graphs In this section, we obtain upper bounds on the HL-index of bipartite graphs in terms of maximum and ...