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Volumn 103, Issue 6, 1996, Pages 470-482

When does A*A = B*B and why does one want to know?

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EID: 0030536935     PISSN: 00029890     EISSN: None     Source Type: Journal    
DOI: 10.2307/2974713     Document Type: Article
Times cited : (21)

References (30)
  • 1
    • 0003070206 scopus 로고
    • Sur les groupes linéaires, réels et orthogonaux
    • L. Autonne, Sur les groupes linéaires, réels et orthogonaux, Bull. Soc. Math. France 30 (1902), 121-134.
    • (1902) Bull. Soc. Math. France , vol.30 , pp. 121-134
    • Autonne, L.1
  • 3
    • 0002275152 scopus 로고
    • Sur les matrices hypohermitiennes et sur les matrices unitaires
    • Nouvelle Série, Fasc.
    • L. Autonne, Sur les matrices hypohermitiennes et sur les matrices unitaires, Annales de l'Université de Lyons, Nouvelle Série, Fasc. 38 (1915), 1-77.
    • (1915) Annales de l'Université de Lyons , vol.38 , pp. 1-77
    • Autonne, L.1
  • 4
  • 5
    • 84968511079 scopus 로고
    • Some new bounds on perturbations of subspaces
    • C. Davis and W. M. Kahan, Some new bounds on perturbations of subspaces, Bull. Amer. Math. Soc. 75 (1969). 863-868.
    • (1969) Bull. Amer. Math. Soc. , vol.75 , pp. 863-868
    • Davis, C.1    Kahan, W.M.2
  • 6
    • 0014751986 scopus 로고
    • The rotation of eigenvectors by a perturbation III
    • C. Davis and W. M. Kahan, The rotation of eigenvectors by a perturbation III, SIAM J. Numer. Analysis 7 (1970), 1-46.
    • (1970) SIAM J. Numer. Analysis , vol.7 , pp. 1-46
    • Davis, C.1    Kahan, W.M.2
  • 7
    • 0040802669 scopus 로고
    • A tree of generalizations of the ordinary singular value decomposition
    • B. De Moor and H. Zha, A tree of generalizations of the ordinary singular value decomposition, Linear Algebra Appl. 147 (1991), 469-500.
    • (1991) Linear Algebra Appl. , vol.147 , pp. 469-500
    • De Moor, B.1    Zha, H.2
  • 8
    • 57849129611 scopus 로고
    • A principal axis transformation for non-Hermitian matrices
    • C. Eckart and G. Young, A principal axis transformation for non-Hermitian matrices, Bull. Amer. Math. Soc. 45 (1939), 118-121.
    • (1939) Bull. Amer. Math. Soc. , vol.45 , pp. 118-121
    • Eckart, C.1    Young, G.2
  • 9
    • 84941391139 scopus 로고
    • Ueber die entwickelung reeler functionen in reihen mittelst der methode der kleinsten quadrate
    • J. P. Gram, Ueber die Entwickelung reeler Functionen in Reihen mittelst der Methode der kleinsten Quadrate, J. für reine angew. Math. (Crelle's Journal) 94 (1883), 41-73.
    • (1883) J. für Reine Angew. Math. (Crelle's Journal) , vol.94 , pp. 41-73
    • Gram, J.P.1
  • 10
    • 0007191085 scopus 로고
    • Singular values and the spectral theorem
    • K. Hoecksmann, Singular values and the spectral theorem, Amer. Math. Monthly 97 (1990), 413-414.
    • (1990) Amer. Math. Monthly , vol.97 , pp. 413-414
    • Hoecksmann, K.1
  • 11
    • 0038725791 scopus 로고
    • A characterization of unitary congruence
    • Y. Hong and R. A. Horn, A characterization of unitary congruence, Linear Multilinear Algebra 25 (1989), 105-119.
    • (1989) Linear Multilinear Algebra , vol.25 , pp. 105-119
    • Hong, Y.1    Horn, R.A.2
  • 14
    • 0000107975 scopus 로고
    • Relations between two sets of variates
    • H. Hotelling, Relations between two sets of variates, Biometrika 28 (1936), 321-377.
    • (1936) Biometrika , vol.28 , pp. 321-377
    • Hotelling, H.1
  • 15
    • 0009290262 scopus 로고
    • Mémoire sur les formes bilinéaires
    • C. Jordan, Mémoire sur les formes bilinéaires, J. Math. Pures Appl. (2) 19 (1874), 35-54.
    • (1874) J. Math. Pures Appl. (2) , vol.19 , pp. 35-54
    • Jordan, C.1
  • 16
    • 0003769554 scopus 로고
    • J. Springer, Berlin, reprinted by Chelsea Publishing Company, New York
    • C. C. MacDuffee, The Theory of Matrices, J. Springer, Berlin, 1933; reprinted by Chelsea Publishing Company, New York, 1946.
    • (1933) The Theory of Matrices
    • MacDuffee, C.C.1
  • 18
    • 0009979847 scopus 로고
    • On multivariate distribution theory
    • I. Olkin and S. N. Roy, On multivariate distribution theory, Ann. Math. Statist. 25 (1954), 329-339.
    • (1954) Ann. Math. Statist. , vol.25 , pp. 329-339
    • Olkin, I.1    Roy, S.N.2
  • 19
    • 0001129014 scopus 로고
    • Towards a generalized value decomposition
    • C. C. Paige and M. A. Saunders, Towards a generalized value decomposition, SIAM J. Numer. Anal. 18 (1981), 398-405.
    • (1981) SIAM J. Numer. Anal. , vol.18 , pp. 398-405
    • Paige, C.C.1    Saunders, M.A.2
  • 20
    • 7544236723 scopus 로고
    • History and generality of the CS decomposition
    • C. C. Paige and M. Wei, History and generality of the CS decomposition, Linear Algebra Appl. 208/209 (1994), 303-326.
    • (1994) Linear Algebra Appl. , vol.208-209 , pp. 303-326
    • Paige, C.C.1    Wei, M.2
  • 21
    • 84972534130 scopus 로고
    • The characteristic roots of matrices
    • W. V. Parker, The characteristic roots of matrices, Duke Math. J. 12 (1945), 519-526.
    • (1945) Duke Math. J. , vol.12 , pp. 519-526
    • Parker, W.V.1
  • 22
    • 34250957105 scopus 로고
    • Zur theorie der linearen und nichtlinearen integralgleichungen
    • E. Schmidt, Zur Theorie der linearen und nichtlinearen Integralgleichungen, Math. Annalen 63 (1907), 433-476.
    • (1907) Math. Annalen , vol.63 , pp. 433-476
    • Schmidt, E.1
  • 23
    • 0000627176 scopus 로고
    • On the perturbation of pseudo-inverses, projections, and linear least squares problems
    • G. W. Stewart, On the perturbation of pseudo-inverses, projections, and linear least squares problems, SIAM Review 19 (1977), 634-662.
    • (1977) SIAM Review , vol.19 , pp. 634-662
    • Stewart, G.W.1
  • 24
    • 34250230826 scopus 로고
    • Computing the CS decomposition of a partitioned orthogonal matrix
    • G. W. Stewart, Computing the CS decomposition of a partitioned orthogonal matrix, Numer. Math. 40 (1982), 297-306.
    • (1982) Numer. Math. , vol.40 , pp. 297-306
    • Stewart, G.W.1
  • 25
    • 0027879547 scopus 로고
    • On the early history of the singular value decomposition
    • G. W. Stewart. On the early history of the singular value decomposition, SIAM Review 35 (1993), 551-566.
    • (1993) SIAM Review , vol.35 , pp. 551-566
    • Stewart, G.W.1
  • 26
    • 0016926423 scopus 로고
    • Generalizing the singular value decomposition
    • C. VanLoan, Generalizing the singular value decomposition, SIAM J. Numer. Anal. 13 (1976), 76-83.
    • (1976) SIAM J. Numer. Anal. , vol.13 , pp. 76-83
    • VanLoan, C.1
  • 27
    • 84968476512 scopus 로고
    • Canonical positive definite matrices under internal linear transformations
    • B. Vinograde, Canonical positive definite matrices under internal linear transformations, Proc. Amer. Math. Soc. 1 (1950), 159-161.
    • (1950) Proc. Amer. Math. Soc. , vol.1 , pp. 159-161
    • Vinograde, B.1
  • 28
    • 0011039516 scopus 로고
    • Zur theorie der bilinearen und quadratischen formen
    • K. Weierstrass, Zur Theorie der bilinearen und quadratischen Formen, Monatsber. Akad. Wiss. Berlin (1868), 310-338.
    • (1868) Monatsber. Akad. Wiss. Berlin , pp. 310-338
    • Weierstrass, K.1
  • 29
    • 0039616534 scopus 로고
    • A polar representation of singular matrices
    • J. Williamson, A polar representation of singular matrices, Bull. Amer. Math. Soc. 41 (1935), 118-123.
    • (1935) Bull. Amer. Math. Soc. , vol.41 , pp. 118-123
    • Williamson, J.1
  • 30
    • 0039616535 scopus 로고
    • On a polar representation of non-singular square matrices
    • A. Wintner and F. D. Murnaghan, On a polar representation of non-singular square matrices, Proc. National Acad. Sciences USA 17 (1931), 676-678.
    • (1931) Proc. National Acad. Sciences USA , vol.17 , pp. 676-678
    • Wintner, A.1    Murnaghan, F.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.