On the generation of correlation matrices.
Budden, Mark, Hadavas, Paul, Hoffman, Lorrie (2008)
Applied Mathematics E-Notes [electronic only]
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Displaying similar documents to “Density of safe matrices.”
On the generation of correlation matrices.
The spectral laws of Hermitian block-matrices with large random blocks.
Oraby, Tamer F. (2007)
Electronic Communications in Probability [electronic only]
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Smallest singular value of sparse random matrices
Alexander E. Litvak, Omar Rivasplata (2012)
Studia Mathematica
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We extend probability estimates on the smallest singular value of random matrices with independent entries to a class of sparse random matrices. We show that one can relax a previously used condition of uniform boundedness of the variances from below. This allows us to consider matrices with null entries or, more generally, with entries having small variances. Our results do not assume identical distribution of the entries of a random matrix and help to clarify the role of the variances...
Generating valid correlation matrices.
Budden, Mark, Hadavas, Paul, Hoffman, Lorrie, Pretz, Chris (2007)
Applied Mathematics E-Notes [electronic only]
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Concentration of the spectral measure of large Wishart matrices with dependent entries.
Guntuboyina, Adityanand, Leeb, Hannes (2009)
Electronic Communications in Probability [electronic only]
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Wigner theorems for random matrices with dependent entries: ensembles associated to symmetric spaces and sample covariance matrices.
Hofmann-Credner, Katrin, Stolz, Michael (2008)
Electronic Communications in Probability [electronic only]
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A simple cocyclic Jacket matrices.
Lee, Moon Ho, Feng, Gui-Liang, Chen, Zhu (2008)
Mathematical Problems in Engineering
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Large deviations and stochastic calculus for large random matrices.
Guionnet, Alice (2004)
Probability Surveys [electronic only]
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Characterization of α1 and α2-matrices
Rafael Bru, Ljiljana Cvetković, Vladimir Kostić, Francisco Pedroche (2010)
Open Mathematics
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This paper deals with some properties of α1-matrices and α2-matrices which are subclasses of nonsingular H-matrices. In particular, new characterizations of these two subclasses are given, and then used for proving algebraic properties related to subdirect sums and Hadamard products.
Poisson statistics for the largest eigenvalues of Wigner random matrices with heavy tails.
Soshnikov, Alexander (2004)
Electronic Communications in Probability [electronic only]
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Combinatorial aspects of generalized complementary basic matrices
Miroslav Fiedler, Frank Hall (2013)
Open Mathematics
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This paper extends some properties of the generalized complementary basic matrices, in particular, in a combinatorial direction. These include inheritance (such as for Alternating Sign Matrices), spectral, and sign pattern matrix (including sign nonsingularity) properties.
Condition numbers of Hessenberg companion matrices
Michael Cox, Kevin N. Vander Meulen, Adam Van Tuyl, Joseph Voskamp (2024)
Czechoslovak Mathematical Journal
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The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized by a Hessenberg form. We demonstrate that the Hessenberg form of the Fiedler companion matrices provides a straight-forward way to compare the condition numbers of these matrices. We also show that there are other companion matrices which can provide a much smaller condition...
Pentadiagonal Companion Matrices
Brydon Eastman, Kevin N. Vander Meulen (2016)
Special Matrices
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The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find...