TY - JOUR T1 - Sonlu Tane İnvolutif Matrisin Toplamının Rankı Üzerine Bir Çalışma AU - Petik, Tuğba AU - Duran, Gülsemin Betül PY - 2015 DA - June DO - 10.20854/befmbd.19860 JF - Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi JO - BUJSE PB - Beykent Üniversitesi WT - DergiPark SN - 1307-3818 SP - 51 EP - 62 VL - 8 IS - 1 LA - tr AB - 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. KW - idempotent matris; involutif matris; rank N2 - 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 CR - KAYNAKLAR CR - Gross J. and Trenkler G., “Nonsingularity of the difference of two CR - oblique projectors”, SIAM Journal on Matrix Analysis and CR - Applications, 1999, 21, 390-395. CR - Koliha J. J., Rakočević V., “Invertibility of the difference of CR - idempotents, Linear and Multilinear Algebra”, 2003, 51, 97-110. CR - Koliha J.J., Rakočević V., “Invertibility of the sum of idempotents, CR - Linear and Multilinear Algebra”, 2002, 50, 285-292. CR - Koliha J. J., Rakočević V., Straškraba I., “The difference and sum of CR - projectors”, Linear Algebra Appl., 2004, 388, 279-288. CR - Koliha J. J., Rakočević V., “The nullity and rank of linear CR - combinations of idempotent matrices”, Linear Algebra Appl., 2006, CR - , 11-14. CR - Marsaglia G., Styan G.P.H., “Equalities and inequalities for ranks of CR - matrices”, Linear and Multilinear Algebra, 1974, 2, 269-292. CR - Tian Y., Styan G.P.H., “Rank equalities for idempotent and involutory CR - matrices”, Linear Algebra App”., 2001, 335, 101-117. CR - Tian Y., Styan G.P.H., “Rank equalities for idempotent matrices with CR - applications”, Journal of Computational and Applied Mathematics, CR - , 191, 77-97. CR - Tian Y., Styan G.P.H., “A new rank formula for idempotent matrices CR - with applications”, Comment. Math. Univ. Carolinae, 2002, 43, 379- CR - Chen M., Chen Q., Li Q., and Yang Z., “On the open problem related CR - to rank equalities for the sum of finitely many idempotent matrices CR - and its applications”, Hindawi Publishing Corporation, The Scientific CR - World Journal, 2014, Article ID 702413, 7 pages. CR - Puntanen S., Styan G.P.H., Historical Introduction: Issai Schur and the CR - Early Development of the Schur Complement, Zhang F. (Ed.), The CR - Schur Complement And Its Applications (1-16), USA, 2005. UR - https://doi.org/10.20854/befmbd.19860 L1 - https://dergipark.org.tr/tr/download/article-file/43817 ER -