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Original Articles

Concavity of certain functions of matrices

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Pages 155-164 | Received 02 Apr 1984, Accepted 09 Aug 1984, Published online: 30 May 2007

References

  • Ando , T. 1979 . Concavity ot certain maps on positive definite matrices and applications to Hadamard products . Linear Algebra and its Applications , 26 : 203 – 241 .
  • Ando , T. 1981 . Inequalities for permanents . Hokkaido Mathematics Journal , 10 : 18 – 36 . Special Issue
  • Davis , Ch. 1959 . Various averaging operations onto subalgebras . Illinois Journal of Mathematics , 3 : 538 – 553 .
  • Davis , Ch. 1963 . Notions generalizing convexity for functions defined on spaces of matrices. Proceedings of Symposia in Pure Mathematics . Convexity , 7 : 187 – 201 .
  • Donoghue , W. 1974 . Monotone Matrix Functions and Analytic Continuation , Springer .
  • Greub , W. W. 1967 . Multilinear Algebra , New York : Springer .
  • Lieb , E.H. 1976 . Inequalities for some operator and matrix functions . Advances in Mathematics , 20 : 174 – 178 .
  • Marcus , M. 1973 and 1975 . Finite Dimensional Algebra , New York : Dekker .
  • Marcus , M. and Lopes , L. 1957 . Inequalities for symmetric functions abd Hermitian matrices . Canadian Journal of Mathematics , 9 : 305 – 312 .
  • Marcus , M. and Minc , H. 1964 . A Survey of Matrix Theory and Matrix Inequalities , Boston : Allyn & Bacon .
  • Marshall , A.W. and Olkin , I. 1982 . A convexity proof of Hadamard's inequality . American Mathematical Monthly , 89 : 687 – 688 .
  • Merris , R. 1979 . Extensions of the Minkowski determinant theorem . Portugaliae Mathematica , 38 : 149 – 153 .
  • Merris , R. 1983 . Extensions of the Hadamard determinant theorem . Israel Journal of Mathematics , 46 : 301 – 304 .
  • 1955 . An Introduction to Linear Algebra Oxford
  • Nakamura , M. and Umegaki , H. 1962 . On von Neumann's theory of measurements in quantum statistics . Mathematica Japonicae , 7 : 151 – 157 .
  • Oppenheim , A. 1954 . Inequalities connected with definite Hermitian forms . American Mathematical Monthly , 61 ( II ) : 463 – 466 .
  • Ostrowski , A. 1952 . Sur quelques applications des fonctions convexes et concaves au sens de I. Schur . Journal des Mathématiques Pures et Appliquées , 31 ( 9 ) : 253 – 292 .
  • Reed , M. and Simon , B. 1978 . “ Methods of Modern Mathematical Physics ” . In Analysis of Operators , New York : Academic Press .

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