Eigenvalues of Nonnegative Symmetric Matrices
By Miroslav Fiedler. 1974
Abstract Some necessary and some sufficient conditions are found for n real numbers to be eigenvalues of an n × n nonnegative (or alternatively, positive) symmetric matrix and for 2 n real numbers to be eigenvalues and diagonal entries of an n × n nonnegative symmetric matrix.
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Citations in the corpus
- Cooperative SGD: A unified Framework for the Design and Analysis of Communication-Efficient SGD Algorithms (2018, neutral): “Lemma 10 ((Fiedler, 1974)) .”
- Existence and construction of nonnegative matrices with prescribed spectrum (2003, background): “Fiedler [3] proved that the Kellogg conditions are sufficient for σ to be the spectrum of some (N + 1) × (N + 1) symmetric nonnegative matrix.”
- Structured inverse eigenvalue problems (2002, unknown): “The first systematic treatment of eigenvalues of symmetric nonnegative matrices probably should be attributed to (Fiedler 1974).”
- The spectra of nonnegative integer matrices via formal power series (2000, background): “Authors have studied the case where the ntuple is comprised of real numbers [Bor95, Cia68, Fri78, Kel71, Per53, Sal72, Sou83, Sul49], the case where the matrices under consideration are symmetric [ Fie74 , JLL96], and the general problem [Joh81, LM99, LL79, Rea94, Rea96, Wuw97].”