메뉴 건너뛰기




Volumn 140, Issue 3, 2012, Pages 987-998

Condition number of a square matrix with I.I.D. Columns drawn from a convex body

Author keywords

Condition number; Convex bodies; Isotropic distributions; Log concave distributions; Norm of a random matrix; Random matrix; Smallest singular number

Indexed keywords


EID: 82255194053     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-2011-10994-8     Document Type: Article
Times cited : (17)

References (17)
  • 1
    • 49649124324 scopus 로고    scopus 로고
    • Smallest singular value of random matrices with independent columns
    • MR2441920 (2009h:15009)
    • R. Adamczak, O. Guédon, A.E. Litvak, A. Pajor, N. Tomczak-Jaegermann, Smallest singular value of random matrices with independent columns, C. R. Math. Acad. Sci. Paris 346 (2008), no. 15-16, 853-856. MR2441920 (2009h:15009)
    • (2008) C. R. Math. Acad. Sci. Paris , vol.346 , Issue.15-16 , pp. 853-856
    • Adamczak, R.1    Guédon, O.2    Litvak, A.E.3    Pajor, A.4    Tomczak-Jaegermann, N.5
  • 2
    • 77749271023 scopus 로고    scopus 로고
    • Quantitative estimates of the convergence of the empirical covariance matrix in log-concave Ensembles
    • MR2601042 (2011c:60019)
    • R. Adamczak, A.E. Litvak, A. Pajor, N. Tomczak-Jaegermann, Quantitative estimates of the convergence of the empirical covariance matrix in log-concave Ensembles, J. Amer. Math. Soc. 23 (2010), no. 2, 535-561. MR2601042 (2011c:60019)
    • (2010) J. Amer. Math. Soc , vol.23 , Issue.2 , pp. 535-561
    • Adamczak, R.1    Litvak, A.E.2    Pajor, A.3    Tomczak-Jaegermann, N.4
  • 3
    • 82255180996 scopus 로고    scopus 로고
    • Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling, Constructive Approximation, to appear (available online)
    • R. Adamczak, A. Litvak, A. Pajor, N. Tomczak-Jaegermann, Restricted isometry property of matrices with independent columns and neighborly polytopes by random sampling, Constructive Approximation, to appear (available online).
    • Adamczak, R.1    Litvak, A.2    Pajor, A.3    Tomczak-Jaegermann, N.4
  • 4
    • 34250424671 scopus 로고
    • Convex measures on locally convex spaces
    • MR0388475 (52:9311)
    • C. Borell, Convex measures on locally convex spaces, Ark. Mat. 12 (1974), 239-252. MR0388475 (52:9311)
    • (1974) Ark. Mat , vol.12 , pp. 239-252
    • Borell, C.1
  • 5
    • 0001126703 scopus 로고
    • Best constants in Young's inequality, its converse, and its generalization to more than three functions
    • MR0412366 (54:492)
    • H.J. Brascamp, E.H. Lieb, Best constants in Young's inequality, its converse, and its generalization to more than three functions, Adv. Math. 20 (1976), no. 2, 151-173. MR0412366 (54:492)
    • (1976) Adv. Math , vol.20 , Issue.2 , pp. 151-173
    • Brascamp, H.J.1    Lieb, E.H.2
  • 6
    • 0000324960 scopus 로고
    • Eigenvalues and condition numbers of random matrices
    • MR964668 (89j:15039)
    • A. Edelman, Eigenvalues and condition numbers of random matrices, SIAM J. of Matrix Anal. and Applic. 9 (1988), pp. 543-560. MR964668 (89j:15039)
    • (1988) SIAM J. of Matrix Anal. and Applic , vol.9 , pp. 543-560
    • Edelman, A.1
  • 7
    • 82255172437 scopus 로고    scopus 로고
    • Geometric probability and random cotype 2, GAFA, 123-138
    • Springer, Berlin, MR2087156 (2005h:60031)
    • E. Gluskin, V. Milman, Geometric probability and random cotype 2, GAFA, 123-138, Lecture Notes in Math., 1850, Springer, Berlin, 2004. MR2087156 (2005h:60031)
    • (2004) Lecture Notes In Math , pp. 1850
    • Gluskin, E.1    Milman, V.2
  • 8
    • 84972579545 scopus 로고
    • Volume estimates for log-concave densities with application to iterated convolutions
    • MR1346249 (96i:46087)
    • M. Junge, Volume estimates for log-concave densities with application to iterated convolutions, Pacific J. Math. 169 (1995), 107-133. MR1346249 (96i:46087)
    • (1995) Pacific J. Math , vol.169 , pp. 107-133
    • Junge, M.1
  • 9
    • 18644382839 scopus 로고    scopus 로고
    • Smallest singular value of random matrices and geometry of random polytopes
    • MR2146352 (2006g:52009)
    • A. E. Litvak, A. Pajor, M. Rudelson, N. Tomczak-Jaegermann, Smallest singular value of random matrices and geometry of random polytopes, Adv. Math. 195 (2005), 491-523. MR2146352 (2006g:52009)
    • (2005) Adv. Math , vol.195 , pp. 491-523
    • Litvak, A.E.1    Pajor, A.2    Rudelson, M.3    Tomczak-Jaegermann, N.4
  • 10
    • 72549087386 scopus 로고    scopus 로고
    • On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution
    • MR2539559 (2010h:15022)
    • A. Pajor, L. Pastur, On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution, Studia Math. 195 (2009), no. 1, 11-29. MR2539559 (2010h:15022)
    • (2009) Studia Math , vol.195 , Issue.1 , pp. 11-29
    • Pajor, A.1    Pastur, L.2
  • 11
    • 33846813628 scopus 로고    scopus 로고
    • Concentration of mass on convex bodies, Geom
    • MR2276533 (2007k:52009)
    • G. Paouris, Concentration of mass on convex bodies, Geom. Funct. Anal. 16, no. 5 (2006), 1021-1049. MR2276533 (2007k:52009)
    • (2006) Funct. Anal , vol.16 , Issue.5 , pp. 1021-1049
    • Paouris, G.1
  • 12
    • 82755183607 scopus 로고    scopus 로고
    • Small ball probability estimates for log-concave measures
    • to appear)
    • G. Paouris, Small ball probability estimates for log-concave measures, Trans. Amer. Math. Soc. (to appear).
    • Trans. Amer. Math. Soc
    • Paouris, G.1
  • 13
    • 49649108303 scopus 로고    scopus 로고
    • Invertibility of random matrices: Norm of the inverse
    • MR2434885 (2010f:46021)
    • M. Rudelson, Invertibility of random matrices: norm of the inverse, Annals of Math. 168, No. 2 (2008), 575-600. MR2434885 (2010f:46021)
    • (2008) Annals of Math , vol.168 , Issue.2 , pp. 575-600
    • Rudelson, M.1
  • 14
    • 41049114969 scopus 로고    scopus 로고
    • The Littlewood-Offord Problem and invertibility of random matrices
    • MR2407948 (2010g:60048)
    • M. Rudelson, R. Vershynin, The Littlewood-Offord Problem and invertibility of random matrices, Adv. Math. 218, No. 2 (2008), 600-633. MR2407948 (2010g:60048)
    • (2008) Adv. Math , vol.218 , Issue.2 , pp. 600-633
    • Rudelson, M.1    Vershynin, R.2
  • 15
    • 84967770163 scopus 로고
    • On the efficiency of algorithms of analysis
    • MR799791 (86m:65061)
    • S. Smale, On the efficiency of algorithms of analysis, Bull. Amer. Math. Soc. 13 (1985), 87-121. MR799791 (86m:65061)
    • (1985) Bull. Amer. Math. Soc , vol.13 , pp. 87-121
    • Smale, S.1
  • 16
    • 0009400517 scopus 로고
    • Condition numbers of random matrices
    • MR1108773 (92i:65086)
    • S. Szarek, Condition numbers of random matrices, J. Complexity 7 (1991), no. 2, 131-149. MR1108773 (92i:65086)
    • (1991) J. Complexity , vol.7 , Issue.2 , pp. 131-149
    • Szarek, S.1
  • 17
    • 71849089047 scopus 로고    scopus 로고
    • Inverse Littlewood-Offord theorems and the condition number of random discrete matrices
    • MR2480613 (2010j:60110)
    • T. Tao, V. Vu, Inverse Littlewood-Offord theorems and the condition number of random discrete matrices, Annals of Math. 169, No. 2 (2009), 595-632. MR2480613 (2010j:60110)
    • (2009) Annals of Math , vol.169 , Issue.2 , pp. 595-632
    • Tao, T.1    Vu, V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.