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Condition numbers of random matrices. (English) Zbl 0760.15018

The author derives upper and lower bounds differing by a constant multiple for the expectation of the condition number of random \(n\times n\) matrices in the \(L_ p\) norm.
These bounds have been independently obtained by A. Edelman [SIAM J. Matrix Anal. Appl. 9, No. 4, 543-560 (1988; Zbl 0678.15019)] and E. Kostlan [Statistical complexity of numerical linear algebra. Thesis, Berkeley (1985)] recently as the author states.

MSC:

15B52 Random matrices (algebraic aspects)
15A12 Conditioning of matrices
65F35 Numerical computation of matrix norms, conditioning, scaling

Citations:

Zbl 0678.15019
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Full Text: DOI

References:

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