Honeycombs and sums of Hermitian matrices
By Allen Knutson, Terence Tao. 2000
210 citations recorded by the source corpus.
Horn's conjecture, which given the spectra of two Hermitian matrices describes the possible spectra of the sum, was recently settled in the affirmative. In this survey we discuss one of the many steps in this, which required us to introduce a combinatorial gadget called a {\em honeycomb}; the question is then reformulable as about the existence of honeycombs with certain boundary conditions. Another important tool is the connection to the representation theory of the group U(n), by ``classical vs. quantum'' analogies.
View Paper: https://www.semanticscholar.org/paper/6c1f96f5f527c208a386ff8807c2b76d491b71fa
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Citations in the corpus
- Large deviations of the extreme eigenvalues of random deformations of matrices (2010, background): “Therefore, (λ, λ̃, θ) satisfy Horn’s inequalities by [29].”
- Geometric complexity theory III: on deciding nonvanishing of a Littlewood–Richardson coefficient (2012, unknown): “∗Supported by NSF grant CCF-1017760.”
- Convergence of Learning Dynamics in Stackelberg Games (2019, background): “Indeed, it reduces to a fundamental problem in linear algebra in which the relationship between the eigenvalues of the sum of two matrices is largely unknown without assumptions on the structure of the matrices [30].”