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Volumn 42, Issue 2, 2000, Pages 233-246

Extremal characterizations of the Schur complement and resulting inequalities

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MATRIX ALGEBRA;

EID: 0034207358     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036144599337290     Document Type: Article
Times cited : (46)

References (30)
  • 1
    • 0014476598 scopus 로고
    • Conditions for positive and nonnegative definiteness in terms of pseudo-inverse
    • A. ALBERT, Conditions for positive and nonnegative definiteness in terms of pseudo-inverse, SIAM J. Appl. Math., 17 (1969), pp. 434-440.
    • (1969) SIAM J. Appl. Math. , vol.17 , pp. 434-440
    • Albert, A.1
  • 2
    • 0007267337 scopus 로고
    • Shorted operators
    • W. N. ANDERSON, Shorted operators, SIAM J. Appl. Math., 20 (1969), pp. 520-525.
    • (1969) SIAM J. Appl. Math. , vol.20 , pp. 520-525
    • Anderson, W.N.1
  • 3
    • 0014522689 scopus 로고
    • Series and parallel addition of matrices
    • W. N. ANDERSON AND R. J. DUFFIN, Series and parallel addition of matrices, J. Math. Anal. Appl., 26 (1969), pp. 576-594.
    • (1969) J. Math. Anal. Appl. , vol.26 , pp. 576-594
    • Anderson, W.N.1    Duffin, R.J.2
  • 4
    • 0342650072 scopus 로고
    • Symmetric functions means of positive operators
    • W. N. ANDERSON, JR., AND T. D. MORLEY, Symmetric functions means of positive operators, Linear Algebra Appl., 60 (1984), pp. 129-143.
    • (1984) Linear Algebra Appl. , vol.60 , pp. 129-143
    • Anderson W.N., Jr.1    Morley, T.D.2
  • 5
    • 0001079995 scopus 로고
    • Concavity of certain maps on positive definite matrices and applications to Hadamard products
    • T. ANDO, Concavity of certain maps on positive definite matrices and applications to Hadamard products, Linear Algebra Appl., 26 (1979), pp. 203-241.
    • (1979) Linear Algebra Appl. , vol.26 , pp. 203-241
    • Ando, T.1
  • 6
    • 0000862711 scopus 로고
    • Generalized Schur complements
    • T. ANDO, Generalized Schur complements, Linear Algebra Appl., 27 (1979), pp. 173-186.
    • (1979) Linear Algebra Appl. , vol.27 , pp. 173-186
    • Ando, T.1
  • 8
    • 0004151496 scopus 로고    scopus 로고
    • Springer-Verlag, New York
    • R. BHATIA, Matrix Analysis, Springer-Verlag, New York, 1997.
    • (1997) Matrix Analysis
    • Bhatia, R.1
  • 10
    • 0343956141 scopus 로고
    • Six generalized Schur complements
    • C. A. BUTLER AND T. D. MORLEY, Six generalized Schur complements, Linear Algebra Appl., 106 (1988), pp. 259-269.
    • (1988) Linear Algebra Appl. , vol.106 , pp. 259-269
    • Butler, C.A.1    Morley, T.D.2
  • 11
    • 0000741454 scopus 로고
    • What are Schur complements, anyway?
    • D. CARLSON, What are Schur complements, anyway?, Linear Algebra Appl., 74 (1986), pp. 257-275.
    • (1986) Linear Algebra Appl. , vol.74 , pp. 257-275
    • Carlson, D.1
  • 12
    • 0015977083 scopus 로고
    • A generalization of the Schur complement by means of the Moore-Penrose inverse
    • D. CARLSON, E. HAYNSWORTH, AND T. MARKHAM, A generalization of the Schur complement by means of the Moore-Penrose inverse, SIAM J. Appl. Math., 26 (1974), pp. 169-179.
    • (1974) SIAM J. Appl. Math. , vol.26 , pp. 169-179
    • Carlson, D.1    Haynsworth, E.2    Markham, T.3
  • 13
    • 0000583828 scopus 로고
    • Manifestations of the Schur complement
    • R. W. COTTLE, Manifestations of the Schur complement, Linear Algebra Appl., 8 (1974), pp. 189-211.
    • (1974) Linear Algebra Appl. , vol.8 , pp. 189-211
    • Cottle, R.W.1
  • 14
    • 85037807524 scopus 로고    scopus 로고
    • Eigenvalues of products of matrices and submatrices in certain positivity classes
    • to appear
    • S. FALLAT, C. R. JOHNSON, AND T. L. MARKHAM, Eigenvalues of products of matrices and submatrices in certain positivity classes, Linear and Multilinear Algebra, to appear.
    • Linear and Multilinear Algebra
    • Fallat, S.1    Johnson, C.R.2    Markham, T.L.3
  • 15
    • 0042570500 scopus 로고    scopus 로고
    • Some results on the Bergstrom and Minkowskii inequalities
    • M. FIEDLER AND T. MARKHAM, Some results on the Bergstrom and Minkowskii inequalities, Linear Algebra Appl., 232 (1996), pp. 199-211.
    • (1996) Linear Algebra Appl. , vol.232 , pp. 199-211
    • Fiedler, M.1    Markham, T.2
  • 17
    • 84968518985 scopus 로고
    • Applications of an inequality for the Schur complement
    • E. V. HAYNSWORTH, Applications of an inequality for the Schur complement, Proc. Amer. Math. Soc., 24 (1970), pp. 512-516.
    • (1970) Proc. Amer. Math. Soc. , vol.24 , pp. 512-516
    • Haynsworth, E.V.1
  • 18
    • 84972535302 scopus 로고
    • Eigenvalues of sums of Hermitian matrices
    • A. HORN, Eigenvalues of sums of Hermitian matrices, Pacific J. Math., 12 (1962), pp. 225-241.
    • (1962) Pacific J. Math. , vol.12 , pp. 225-241
    • Horn, A.1
  • 21
    • 54649083948 scopus 로고    scopus 로고
    • Stable bundles, representation theory and Hermitian operators
    • A. A. KLYACHKO. Stable bundles, representation theory and Hermitian operators, Selecta Math. (N.S.), 3 (1998), pp. 419-445.
    • (1998) Selecta Math. (N.S.) , vol.3 , pp. 419-445
    • Klyachko, A.A.1
  • 22
    • 0000346864 scopus 로고
    • The theory of self adjoint extensions of semibounded Hermitian transformations and its applications I
    • Russian with English summary
    • M. G. KREIN, The theory of self adjoint extensions of semibounded Hermitian transformations and its applications I, Mat. Sb., 20 (1947), pp. 431-495 (Russian with English summary).
    • (1947) Mat. Sb. , vol.20 , pp. 431-495
    • Krein, M.G.1
  • 23
    • 21744446425 scopus 로고    scopus 로고
    • A minimum principle, and estimates of eigenvalues for Schur complements of positive semidefinite matrices
    • J. LIU AND L. ZHU, A minimum principle, and estimates of eigenvalues for Schur complements of positive semidefinite matrices. Linear Algebra Appl., 265 (1997), pp. 123-145.
    • (1997) Linear Algebra Appl. , vol.265 , pp. 123-145
    • Liu, J.1    Zhu, L.2
  • 24
    • 0042638218 scopus 로고    scopus 로고
    • A Schur complement inequality for certain P-matrices
    • T. MARKHAM AND R. SMITH, A Schur complement inequality for certain P-matrices, Linear Algebra Appl., 281 (1998), pp. 33-41.
    • (1998) Linear Algebra Appl. , vol.281 , pp. 33-41
    • Markham, T.1    Smith, R.2
  • 26
    • 0013314516 scopus 로고
    • Concavity of monotone matrix functions of finite order
    • R. MATHIAS, Concavity of monotone matrix functions of finite order, Linear and Multilinear Algebra, 27 (1990), pp. 129-138.
    • (1990) Linear and Multilinear Algebra , vol.27 , pp. 129-138
    • Mathias, R.1
  • 27
    • 0002242889 scopus 로고
    • On the eigenvalues of sums of Hermitian matrices
    • R. C. THOMPSON AND L. J. FREEDE, On the eigenvalues of sums of Hermitian matrices, Linear Algebra Appl., 4 (1971), pp. 369-376.
    • (1971) Linear Algebra Appl. , vol.4 , pp. 369-376
    • Thompson, R.C.1    Freede, L.J.2
  • 28
    • 0039014426 scopus 로고
    • On the singular values of a matrix product-I, II, III
    • R. C. THOMPSON AND S. THERIANOS, On the singular values of a matrix product-I, II, III, Scripta Math., 29 (1973), pp. 99-123.
    • (1973) Scripta Math. , vol.29 , pp. 99-123
    • Thompson, R.C.1    Therianos, S.2
  • 29
    • 21944457085 scopus 로고    scopus 로고
    • Schur complements and matrix inequalities of Hadamard products
    • B.-Y. WANG AND F. ZHANG, Schur complements and matrix inequalities of Hadamard products, Linear and Multilinear Algebra, 43 (1997), pp. 315-326.
    • (1997) Linear and Multilinear Algebra , vol.43 , pp. 315-326
    • Wang, B.-Y.1    Zhang, F.2
  • 30


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