188
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications

Pages 1237-1246 | Received 19 Mar 2010, Accepted 23 May 2010, Published online: 15 Apr 2011

References

  • Anderson , TW and Styan , GPH . “ Cochran's theorem, rank additivity and tripotent matrices ” . In Statistics and Probability: Essays in Honor of C.R. Rao , Edited by: Kallianpur , G , Krishnaiah , PR and Ghosh , JK . 1 – 23 . Amsterdam : North-Holland . (Reprinted in The Collected Papers of T.W. Anderson, Vol. 2, Wiley, New York, 1990, pp. 1307–1329)
  • Baksalary , JK and Baksalary , OM . 2000 . Idempotency of linear combinations of two idempotent matrices . Linear Algebra Appl. , 321 : 3 – 7 .
  • Baksalary , JK and Baksalary , OM . 2006 . When is a linear combination of two idempotent matrices the group involutory matrix? . Linear Multilinear Algebra , 54 : 429 – 435 .
  • Baksalary , JK , Baksalary , OM and Özdemir , H . 2004 . A note on linear combinations of commuting tripotent matrices . Linear Algebra Appl. , 388 : 45 – 51 .
  • Beńitez , J and Thome , N . 2005 . Idempotency of linear combinations of an idempotent matrix and t-potent matrix that commute . Linear Algebra Appl. , 403 : 414 – 418 .
  • Coll , C and Thome , N . 2003 . Oblique projectors and group involutory matrices . Appl. Math. Comput. , 140 : 517 – 522 .
  • Graybill , FA . 1969 . Introduction to Matrices with Applications in Statistics , California : Wadsworth Publishing Company Inc. .
  • Mathai , AM and Provost , SB . 1992 . Quadratic Forms in Random Variables: Theory and Applications , New York : Marcel Dekker .
  • Özdemir , H and Özban , AY . 2004 . On idempotency of linear combinations of idempotent matrices . Appl. Math. Comput. , 159 : 439 – 448 .
  • Özdemir , H and Sarduvan , M . 2008 . Notes on linear combinations of two tripotent, idempotent, and involutive matrices that commute . An. St. Univ. Ovidius Constanta , 16 : 83 – 90 .
  • Özdemir , H , Sarduvan , M , Özban , AY and Güler , N . 2009 . On idempotency and tripotency of linear combinations of two commuting tripotent matrices . Appl. Math. Comput. , 207 : 197 – 201 .
  • Sarduvan , M and Özdemir , H . 2008 . On linear combinations of two tripotent, idempotent, and involutive matrices . Appl. Math. Comput. , 200 : 401 – 406 .
  • Spitkovsky , IM . 1994 . Once more on algebras generated by two projections . Linear Algebra Appl. , 208/209 : 377 – 395 .
  • Spitkovsky , IM . 2006 . On polynomials in two projections . Electron. J. Linear Algebra , 15 : 154 – 158 .
  • Tian , Y . 2010 . Two universal similarity factorization equalities for commutative involutory and idempotent matrices and their applications . Linear Multilinear Algebra , 59 : 129 – 144 .
  • Vasilevsky , N and Spitkovsky , IM . 1981 . On the algebra generated by two projections . Dokl. Akad. Nauk Ukrain. SSR, Ser. A , 8 : 10 – 13 .

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.