ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

20th Conference of the International Linear Algebra Society (ILAS)

20th ILAS Conference

In minisymposium: Matrix Inequalities and Operator Means

Mon 11:00–11:30, Room AV 03.12
Some Remarks on Positive Semidefinite Matrices
Ramazan Turkmen (Selcuk University, Konya-Turkey)

In recent years, Positive semidefinite matrices expecialy $2\times 2$ positive semidefinite are very popular. A lot of authors have obtained some nice inequalities about eigenvalues, singular values, trace, determinant, unitarily invariant norms using the properties of this matrices, majorization and classical inequalities . In this thalk, we give some known results for positive semidefinite matrices and in the light of this results, we present some remarks for positive semidefinite and PPT matrices.

  1. X. Zhan, 2002, Matrix Inequalities, Springer-Verlag, Berlin.
  2. \justifying F. Zhang, 2010, Matrix Theory: Basic Results and Techniques, Springer, New York.
  3. \justifying A. W. Marshall, I. Olkin, 2011 Inequalities: Theory of Majorization and Its Applications, Academic Press.
  4. \justifying Turkmen, R., Paksoy, V. E., and Zhang, F., 2012, Some inequalities of majorization type, Linear Algebra and its Applications 437(6), 1305-1316.
  5. \justifying Y. Tao, 2006, More results on singular value inequalities of matrices, Linear Algebra and its Applications, 416, 724-729.
  6. \justifying F. Zhang, 2001, Matrix Inequalities by Means of Block Matrices, Mathematical Inequalities and Applications,Vol. 4, Number 4, pp. 481-490.
  7. \justifying R. Bhatia, 2007, Positive Definite Matrices. Priceton University Press, Priceton.
  8. \justifying M. Lin, Remarks on two recent results of Audenaert, Linear Algebra and its Applications 489 (2016) 24–29.