The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Eigenvalues and Condition Numbers of Random Matrices
Open accessAbstract
Given a random matrix, what condition number should be expected? This paper presents a proof that for real or complex $n \times n$ matrices with elements from a standard normal distribution, the expected value of the log of the 2-norm condition number is asymptotic to $\log n$ as $n \to \infty$. In fact, it is roughly $\log n + 1.537$ for real matrices and $\log n + 0.982$ for complex matrices as $n \to \infty$. The paper discusses how the distributions of the condition numbers behave for large n for real or complex and square or rectangular matrices. The exact distributions of the condition numbers of $2 \times n$ matrices are also given. Intimately related to this problem is the distribution of the eigenvalues of Wishart matrices. This paper studies in depth the largest and smallest eigenvalues, giving exact distributions in some cases. It also describes the behavior of all the eigenvalues, giving an exact formula for the expected characteristic polynomial.
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Cites
Handbook of Mathematical Functions
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DISTRIBUTION OF EIGENVALUES FOR SOME SETS OF RANDOM MATRICES
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Distributions of Matrix Variates and Latent Roots Derived from Normal Samples
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A Limit Theorem for the Norm of Random Matrices
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Analysis of Discrete Ill-Posed Problems by Means of the L-Curve
Hansen, P. C. (1992) · SIAM Review · doi:10.1137/1034115 · Cited by 3,903
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Metadata
- Authors
- Edelman, A.
- Venue
- SIAM Journal on Matrix Analysis and Applications
- Published
- 1988-10
- Volume
- 9
- Issue
- 4
- Pages
- 543-560
- ISSN
- 0895-4798 (ISSN-L)
- 1095-7162
- OpenAlex
- W1974755392
- Cited by
- 1,284
- References
- 14
- FWCI
- 3.95
- Type
- journal article
- Language
- en
- Open access
- green
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- Edelman, A. (1988). Eigenvalues and Condition Numbers of Random Matrices. SIAM Journal on Matrix Analysis and Applications. https://doi.org/10.1137/0609045
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
