Matrix Analysis, 2nd Ed

By Roger A. Horn, Charles R. Johnson. 2012

1,763 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a55cfa24f6309d2e67c14629e8da7ab43cf4fa5c

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In Computational Theory and Mathematics

Citations in the corpus

CayleyNets: Graph Convolutional Neural Networks With Complex Rational Spectral Filters (2017, neutral): “By Levy–Desplanques theorem ([40] Theorem 6.”
Maximizing diversity in biology and beyond (2015, neutral): “1 of [39]), every eigenvalue of Z is in the interval (0, 2).”
Clustering algorithms: A comparative approach (2016, background): “A valid covariance matrix must be positive semi-definite [95], which is hard to ensure.”
Violation of detailed balance accelerates relaxation. (2013, background): “The essence of the proof for proposition (I) is the Ostrowski-Taussky inequality [29].”
Strong SOCP Relaxations for the Optimal Power Flow Problem (2015, methodology): “We can further apply SOCP relaxation to the SDP constraint (8d) by only imposing the following constraints on all the 2 × 2 submatrices of X for each line ( i, j ) ∈ L , This is a relaxation of (8d), because (8d) requires all principal submatrices of X be SDP (see e.g., Horn and Johnson (2013)).”
Gradient Descent with Identity Initialization Efficiently Learns Positive-Definite Linear Transformations by Deep Residual Networks (2018, neutral): “Lemma 4 (Horn & Johnson 2013) .”
Detailed study of Gaussian boson sampling (2018, methodology): “This construction, if we can control both TGBS and each rj , means that we can generate any (rescaled) symmetric matrix B by use of the Autonne-Takagi decomposition [37].”
Efficient CUF-based FEM analysis of thin-wall structures with Lagrange polynomial expansion (2020, background): “, the smallest eigenvalue and the associated eigenfunction of the system Rayliegh quotients [24, 25] Known as Rayliegh-Ritz ration, which is defined for Hermitian matrix.”
Probability on Trees and Networks (2017, background): “A cleaner way to say that they are “close” to Cayley graphs was noted by Godsil, Imrich, Seifter, Watkins, and Woess (1989) as a consequence of results by Trofimov (1984) and Sabidussi (1964): every transitive graph G of polynomial growth has the property that for some n ≥ 1, the graph nG is a Cayle”
Optimization over time-varying directed graphs with row and column-stochastic matrices (2018, neutral): “Proof of Lemma 5 Proof: Based on the successive application of Schur’s determinant identity [52], [58], the characteristic polynomial of M is given by (−1)(λ− 1)(γA−λ)(γB−λ)λ.”