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Volumn 26, Issue 2, 2005, Pages 441-456

Eigenvalues and condition numbers of complex random matrices

Author keywords

Complex random matrix; Complex wishart matrix; Complex zonal polynomials; Condition number distribution; Eigenvalue distribution

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; NUMERICAL ANALYSIS; POLYNOMIALS;

EID: 17444430326     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S089547980342204X     Document Type: Article
Times cited : (96)

References (22)
  • 1
    • 0031535563 scopus 로고    scopus 로고
    • The calogero-sutherland model and generalized classical polynomials
    • T. BAKER AND P. FORRESTER, The Calogero-Sutherland model and generalized classical polynomials, Comm. Math. Phys., 188 (1997), pp. 175-216.
    • (1997) Comm. Math. Phys. , vol.188 , pp. 175-216
    • Baker, T.1    Forrester, P.2
  • 2
    • 0001239018 scopus 로고
    • Some noncentral distribution problems in multivariate analysis
    • A. G. CONSTANTINE, Some noncentral distribution problems in multivariate analysis, Ann. Math. Statist., 34 (1963), pp. 1270-1285.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 1270-1285
    • Constantine, A.G.1
  • 3
    • 0000324960 scopus 로고
    • Eigenvalues and condition numbers of random matrices
    • A. EDELMAN, Eigenvalues and condition numbers of random matrices, SIAM J. Matrix Anal. Appl., 9 (1988), pp. 543-560.
    • (1988) SIAM J. Matrix Anal. Appl. , vol.9 , pp. 543-560
    • Edelman, A.1
  • 4
    • 84968515320 scopus 로고
    • Numerical inverting of matrices of high order II
    • H. H. GOLDSTINE AND J. VON NEUMANN, Numerical inverting of matrices of high order II, Amer. Math. Soc. Proc., 2 (1951), pp. 188-202.
    • (1951) Amer. Math. Soc. Proc. , vol.2 , pp. 188-202
    • Goldstine, H.H.1    Von Neumann, J.2
  • 5
    • 0000952005 scopus 로고
    • Distributions of matrix variate and latent roots derived from normal samples
    • A. T. JAMES, Distributions of matrix variate and latent roots derived from normal samples, Ann. Math. Statist., 35 (1964), pp. 475-501.
    • (1964) Ann. Math. Statist. , vol.35 , pp. 475-501
    • James, A.T.1
  • 6
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. M. JOHNSTONE, On the distribution of the largest eigenvalue in principal components analysis, Ann. Statist., 29 (2001), pp. 295-327.
    • (2001) Ann. Statist. , vol.29 , pp. 295-327
    • Johnstone, I.M.1
  • 7
    • 0001558814 scopus 로고
    • Distribution of the largest or the smallest characteristic root under null hypothesis concerning complex multivariate normal populations
    • C. G. KHATRI, Distribution of the largest or the smallest characteristic root under null hypothesis concerning complex multivariate normal populations, Ann. Math. Statist., 35 (1964), pp. 1807-1810.
    • (1964) Ann. Math. Statist. , vol.35 , pp. 1807-1810
    • Khatri, C.G.1
  • 8
    • 0000624583 scopus 로고
    • On certain distribution problems based on positive definite quadratic functions in normal vectors
    • C. G. KHATRI, On certain distribution problems based on positive definite quadratic functions in normal vectors, Ann. Math. Statist., 37 (1966) pp. 468-479.
    • (1966) Ann. Math. Statist. , vol.37 , pp. 468-479
    • Khatri, C.G.1
  • 9
    • 0040027528 scopus 로고
    • On the non-central distributions of two test criteria in multivariate analysis of variance
    • C. G. KHATRI AND K. C. S. PILLAI, On the non-central distributions of two test criteria in multivariate analysis of variance, Ann. Math. Statist., 39 (1968), pp. 215-226.
    • (1968) Ann. Math. Statist. , vol.39 , pp. 215-226
    • Khatri, C.G.1    Pillai, K.C.S.2
  • 13
    • 0035581413 scopus 로고    scopus 로고
    • On the singular values of Gaussian random matrices
    • J. SHEN, On the singular values of Gaussian random matrices, Linear Algebra Appl., 326 (2001), pp. 1-14.
    • (2001) Linear Algebra Appl. , vol.326 , pp. 1-14
    • Shen, J.1
  • 14
    • 84967770163 scopus 로고
    • On the efficiency of algorithms of analysis
    • S. SMALE, On the efficiency of algorithms of analysis, Bull. Amer. Math. Soc., 13 (1985), pp. 87-121.
    • (1985) Bull. Amer. Math. Soc. , vol.13 , pp. 87-121
    • Smale, S.1
  • 15
    • 45249131043 scopus 로고
    • Some combinatorial properties of Jack symmetric functions
    • R. P. STANLEY, Some combinatorial properties of Jack symmetric functions, Adv. Math., 77, (1989), pp. 76-115.
    • (1989) Adv. Math. , vol.77 , pp. 76-115
    • Stanley, R.P.1
  • 16
    • 0008961547 scopus 로고
    • On the distribution of the largest latent root of the covariance matrix
    • T. SUGIYAMA, On the distribution of the largest latent root of the covariance matrix, Ann. Math. Statist., 38 (1967), pp. 1148-1151.
    • (1967) Ann. Math. Statist. , vol.38 , pp. 1148-1151
    • Sugiyama, T.1
  • 17
    • 0000621358 scopus 로고
    • Joint distribution of the extreme roots of a covariance matrix
    • T. SUGIYAMA, Joint distribution of the extreme roots of a covariance matrix, Ann. Math. Statist., 41 (1970), pp. 655-657.
    • (1970) Ann. Math. Statist. , vol.41 , pp. 655-657
    • Sugiyama, T.1
  • 18
    • 51249190626 scopus 로고
    • Distributions of the largest latent root of the multivariate complex Gaussian distribution
    • T. SUGIYAMA, Distributions of the largest latent root of the multivariate complex Gaussian distribution, Ann. Inst. Statist. Math., 24 (1972), pp. 87-94.
    • (1972) Ann. Inst. Statist. Math. , vol.24 , pp. 87-94
    • Sugiyama, T.1
  • 19
    • 0001252659 scopus 로고
    • Numerical inverting of matrices of high order
    • J. VON NEUMANN AND H. H. GOLDSTINE, Numerical inverting of matrices of high order, Bull. Amer. Math. Soc., 53 (1947), pp. 1021-1099.
    • (1947) Bull. Amer. Math. Soc. , vol.53 , pp. 1021-1099
    • Von Neumann, J.1    Goldstine, H.H.2
  • 20
    • 0001537411 scopus 로고
    • Exact joint density of the largest and smallest roots of the Wishart and MANOVA matrices
    • V. B. WAIKAR AND F. J. SCHUURMANN, Exact joint density of the largest and smallest roots of the Wishart and MANOVA matrices, Util. Math., 4 (1973), pp. 253-260.
    • (1973) Util. Math. , vol.4 , pp. 253-260
    • Waikar, V.B.1    Schuurmann, F.J.2
  • 21
    • 84984390983 scopus 로고
    • On the joint distributions of the largest and smallest latent roots of two random matrices (noncentral case)
    • V. B. WAIKAR, On the joint distributions of the largest and smallest latent roots of two random matrices (noncentral case), South African Statist. J., 7 (1973), pp. 103-108.
    • (1973) South African Statist. J. , vol.7 , pp. 103-108
    • Waikar, V.B.1
  • 22
    • 0001433886 scopus 로고
    • Error analysis revisited
    • J. H. WILKINSON, Error analysis revisited, IMA Bulletin, 22 (1986), pp. 192-200.
    • (1986) IMA Bulletin , vol.22 , pp. 192-200
    • Wilkinson, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.