195
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Distributions of eigenvalues and inertias of some block Hermitian matrices consisting of orthogonal projectors

&
Pages 1027-1069 | Received 29 Jul 2010, Accepted 10 Oct 2011, Published online: 05 Jan 2012

References

  • Afriat , SN . 1957 . Orthogonal and oblique projectors and the characteristics of pairs of vector spaces . Proc. Camb. Phil. Soc. , 53 : 800 – 816 .
  • Avron , J , Seiler , R and Simon , B . 1994 . The index of a pair of projections . J. Funct. Anal. , 120 : 220 – 237 .
  • Baksalary , OM and Trenkler , G . 2009 . Column space equalities for orthogonal projectors . Appl. Math. Comput. , 212 : 519 – 529 .
  • Benítez , J and Rakocěvić , V . 2008 . Applications of CS decomposition in linear combinations of two orthogonal projectors . Appl. Math. Comput. , 203 : 761 – 769 .
  • Benítez , J and Rakocěvić , V . 2010 . On the spectrum of linear combinations of two projections in C*-algebras . Linear Multilinear Algebra , 58 : 673 – 679 .
  • Bjørstad , PE and Mandel , J . 1991 . On the spectra of sums of orthogonal projections with applications to parallel computing . BIT , 31 : 76 – 88 .
  • Borac , S . 1995 . On the algebra generated by two projections . J. Math. Phys. , 36 : 863 – 874 .
  • Böttcher , A and Spitkovsky , IM . 2010 . A gentle guide to the basics of two projections theory . Linear Algebra Appl. , 432 : 1412 – 1459 .
  • Cheng , S and Tian , Y . 2003 . Moore–Penrose inverses of products and differences of orthogonal projectors . Acta Sci. Math. (Szeged) , 69 : 533 – 542 .
  • Davis , C . 1958 . Separation of two linear subspaces . Acta Sci. Math. , 19 : 172 – 187 .
  • Dixmier , J . 1948 . Position relative de deux variétés linéaires fermées dans un espace de Hilbert . Rev. Sci. , 86 : 387 – 399 .
  • Galántai , A . 2004 . Projectors and Projection Methods , Dordrecht : Kluwer Academic Publishers .
  • Galántai , A . 2008 . Subspaces, angles and pairs of orthogonal projections . Linear Multilinear Algebra , 56 : 227 – 260 .
  • Groß , J . 1999 . On the product of orthogonal projectors . Linear Algebra Appl. , 289 : 141 – 150 .
  • Halmos , PR . 1969 . Two subspaces . Trans. Amer. Math. Soc. , 144 : 381 – 389 .
  • Haynsworth , EV . 1968 . Determination of the inertia of a partitioned Hermitian matrix . Linear Algebra Appl. , 1 : 73 – 81 .
  • Haynsworth , EV and Ostrowski , AM . 1968 . On the inertia of some classes of partitioned matrices . Linear Algebra Appl. , 1 : 299 – 316 .
  • Marsaglia , G and Styan , GPH . 1974 . Equalities and inequalities for ranks of matrices . Linear Multilinear Algebra , 2 : 269 – 292 .
  • Nishio , K . 1985 . The structure of a real linear combination of two projections . Linear Algebra Appl. , 66 : 169 – 176 .
  • Oikhberg , T . 1999 . Products of orthogonal projections . Proc. Amer. Math. Soc. , 127 : 3659 – 3669 .
  • Pazzis , CS . 2010 . On linear combinations of two idempotent matrices over an arbitrary field . Linear Algebra Appl. , 433 : 625 – 636 .
  • Popovici , D and Sebestyén , Z . 2009 . On the generalized derivation induced by two projections . Integral Eqns. Oper. Theory , 65 : 285 – 304 .
  • Raeburn , I and Sinclair , AM . 1989 . The C*-algebra generated by two projections . Math. Scand. , 65 : 278 – 290 .
  • Tian , Y . 2010 . Equalities and inequalities for inertias of Hermitian matrices with applications . Linear Algebra Appl. , 433 : 263 – 296 .
  • Tian , Y . 2010 . Equalities for orthogonal projectors and their operations . Centr. Eur. J. Math. , 8 : 855 – 870 .
  • Tian , Y . 2011 . Expansion formulas for the inertias of Hermitian matrix polynomials and matrix pencils of orthogonal projectors . J. Math. Anal. Appl. , 376 : 162 – 186 .
  • Tian , Y and Styan , GPH . 2001 . Rank equalities for idempotent and involutory matrices . Linear Algebra Appl. , 335 : 101 – 117 .
  • Tian , Y and Styan , GPH . 2006 . Rank equalities for idempotent matrices with applications . J. Comput. Appl. Math. , 191 : 77 – 97 .
  • Vasilevsky , N . 1998 . C*-algebras generated by orthogonal projections and their applications . Integral Eqns. Oper. Theory , 31 : 113 – 132 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.