Abstract
Chen M. and et al. have solved an open problem related to rank equalities for the sum of finitely many idempotent matrices using the Gaussian elimination method in [Chen M. and et al., On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications, The Scientific World Journal, 2014]. In this work, it is obtained a similar rank equality for the sum of finitely many involutive matices and derived some results from this equality
References
- KAYNAKLAR
- Gross J. and Trenkler G., “Nonsingularity of the difference of two
- oblique projectors”, SIAM Journal on Matrix Analysis and
- Applications, 1999, 21, 390-395.
- Koliha J. J., Rakočević V., “Invertibility of the difference of
- idempotents, Linear and Multilinear Algebra”, 2003, 51, 97-110.
- Koliha J.J., Rakočević V., “Invertibility of the sum of idempotents,
- Linear and Multilinear Algebra”, 2002, 50, 285-292.
- Koliha J. J., Rakočević V., Straškraba I., “The difference and sum of
- projectors”, Linear Algebra Appl., 2004, 388, 279-288.
- Koliha J. J., Rakočević V., “The nullity and rank of linear
- combinations of idempotent matrices”, Linear Algebra Appl., 2006,
- , 11-14.
- Marsaglia G., Styan G.P.H., “Equalities and inequalities for ranks of
- matrices”, Linear and Multilinear Algebra, 1974, 2, 269-292.
- Tian Y., Styan G.P.H., “Rank equalities for idempotent and involutory
- matrices”, Linear Algebra App”., 2001, 335, 101-117.
- Tian Y., Styan G.P.H., “Rank equalities for idempotent matrices with
- applications”, Journal of Computational and Applied Mathematics,
- , 191, 77-97.
- Tian Y., Styan G.P.H., “A new rank formula for idempotent matrices
- with applications”, Comment. Math. Univ. Carolinae, 2002, 43, 379-
- -
- Chen M., Chen Q., Li Q., and Yang Z., “On the open problem related
- to rank equalities for the sum of finitely many idempotent matrices
- and its applications”, Hindawi Publishing Corporation, The Scientific
- World Journal, 2014, Article ID 702413, 7 pages.
- Puntanen S., Styan G.P.H., Historical Introduction: Issai Schur and the
- Early Development of the Schur Complement, Zhang F. (Ed.), The
- Schur Complement And Its Applications (1-16), USA, 2005.
Abstract
Chen M. and et al. have solved the open problem related to rank equalities for the sum of finitely many idempotent matrices by using the Gussian elimination method (Chen M. and et al. “On the open problem related to rank equalities for the sum of finitely many idempotent matrices and its applications”, The Scientific World Journal, 2014). In this work, it is obtained a similar rank equality for the sum of finitely many involutive matices and derived some results from this equality.
References
- KAYNAKLAR
- Gross J. and Trenkler G., “Nonsingularity of the difference of two
- oblique projectors”, SIAM Journal on Matrix Analysis and
- Applications, 1999, 21, 390-395.
- Koliha J. J., Rakočević V., “Invertibility of the difference of
- idempotents, Linear and Multilinear Algebra”, 2003, 51, 97-110.
- Koliha J.J., Rakočević V., “Invertibility of the sum of idempotents,
- Linear and Multilinear Algebra”, 2002, 50, 285-292.
- Koliha J. J., Rakočević V., Straškraba I., “The difference and sum of
- projectors”, Linear Algebra Appl., 2004, 388, 279-288.
- Koliha J. J., Rakočević V., “The nullity and rank of linear
- combinations of idempotent matrices”, Linear Algebra Appl., 2006,
- , 11-14.
- Marsaglia G., Styan G.P.H., “Equalities and inequalities for ranks of
- matrices”, Linear and Multilinear Algebra, 1974, 2, 269-292.
- Tian Y., Styan G.P.H., “Rank equalities for idempotent and involutory
- matrices”, Linear Algebra App”., 2001, 335, 101-117.
- Tian Y., Styan G.P.H., “Rank equalities for idempotent matrices with
- applications”, Journal of Computational and Applied Mathematics,
- , 191, 77-97.
- Tian Y., Styan G.P.H., “A new rank formula for idempotent matrices
- with applications”, Comment. Math. Univ. Carolinae, 2002, 43, 379-
- -
- Chen M., Chen Q., Li Q., and Yang Z., “On the open problem related
- to rank equalities for the sum of finitely many idempotent matrices
- and its applications”, Hindawi Publishing Corporation, The Scientific
- World Journal, 2014, Article ID 702413, 7 pages.
- Puntanen S., Styan G.P.H., Historical Introduction: Issai Schur and the
- Early Development of the Schur Complement, Zhang F. (Ed.), The
- Schur Complement And Its Applications (1-16), USA, 2005.
Details
| Primary Language | Turkish |
|---|---|
| Journal Section | Articles |
| Authors | |
| Publication Date | April 3, 2015 |
| Published in Issue | Year 2015 |
Cite
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