TY  - JOUR
T1  - Alternative characterizations of some linear combinations of an idempotent matrix and a tripotent matrix that commute
TT  - Değişmeli bir idempotent ve bir tripotent matrisin bazı lineer kombinasyonlarının alternatif karakterizasyonları
AU  - Petik, Tuğba
AU  - Gökmen, Burak Tufan
PY  - 2020
DA  - January
DO  - 10.25092/baunfbed.680775
JF  - Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
JO  - BAUN Fen. Bil. Enst. Dergisi
PB  - Balıkesir University
WT  - DergiPark
SN  - 1301-7985
SP  - 255
EP  - 268
VL  - 22
IS  - 1
LA  - en
AB  - In this work, first, Theorem 2 in [1] [Yao, H., Sun, Y., Xu, C., and Bu, C., A note on linear combinations of an idempotent matrix and a tripotent matrix, J. Appl. Math.  Informatics, 27 (5-6), 1493-1499, 2009] and Theorem 2.2 in [2][Özdemir H., Sarduvan M., Özban A.Y., Güler N., On idempotency and tripotency of linear combinations of two commuting tripotent matrices, Appl. Math. Comput., 207 (1), 197-201, 2009] are reconsidered in different ways under the condition that the matrices involved in the linear combination are commutative. Thus, it is seen that there are some missing results in Theorem 2 in [1]. Then, by considering the obtained results and doing some detailed investigations, it is given a new characterization, without any restriction on the involved matrices except for commutativity, of a linear combination of an idempotent and a tripotent matrix that commute.
KW  - Idempotent matrix
KW  - tripotent matrix
KW  - linear combination
KW  - commutativity
N2  - Bu çalışmada ilk olarak [1][Yao, H., Sun, Y., Xu, C., and Bu, C., A note on linear combinations of an idempotent matrix and a tripotent matrix, J. Appl. Math. Informatics, 27 (5-6), 1493-1499, 2009]’deki Teorem 2 ve [2]([Özdemir H., Sarduvan M., Özban A.Y., Güler N., On idempotency and tripotency of linear combinations of two commuting tripotent matrices, Appl. Math. Comput., 207 (1), 197-201, 2009]’deki Teorem 2.2, lineer kombinasyonda içerilen matrislerin değişmeli olması koşulu altında  farklı tarzlarda yeniden ele alınmaktadır. Böylece, [1]’deki Teorem 2’de bazı eksik sonuçların mevcut olduğu görülmüştür. Daha sonra elde edilen sonuçları göz önüne alarak ve bazı detaylı incelemeler yaparak, değişmeli bir idempotent ve bir tripotent matrisin bir lineer kombinasyonunun, içerilen matrisler üzerinde değişmelilik dışında herhangi bir kısıtlama olmaksızın, yeni bir karakterizasyonu verilmektedir.
CR  - Yao, H., Sun, Y., Xu, C., and  Bu, C., A note on linear combinations of an idempotent matrix and a tripotent matrix, Journal of Applied Mathematics and Informatics,  27, 1493-1499, (2009).
	
Özdemir, H., Sarduvan, M., Özban, A.Y., and Güler, N.,  On idempotency and tripotency of linear combinations of two commuting tripotent matrices, Applied Mathematics and Computation, 207 1, 197-201, (2009).
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CR  - Baksalary, J.K., Baksalary, O.M., and Özdemir, H., A note on linear combinations of commuting tripotent matrices, Linear Algebra and its Applications, 388, 45-51, (2004).
CR  - Benítez, J. and Thome, N., Idempotency of linear combinations of an idempotent matrix and a t-potent matrix that commute, Linear Algebra and its Applications, 403, 414-418, (2005).
CR  - Benítez, J. and Thome, N., Idempotency of linear combinations of an idempotent matrix and a t-potent matrix that do not commute, Linear and Multilinear Algebra, 56, 6, 679-687, (2008).
CR  - Sarduvan, M. and Özdemir, H., On linear combinations of two tripotent, idempotent and involutive matrices, Applied Mathematics and Computation, 200, 401-406, (2008).
CR  - Uç, M., Özdemir, H., and Özban, A.Y., On the quadraticity of linear combinations of quadratic matrices, Linear and Multilinear Algebra, 63, 6, 1125-1137, (2015).
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UR  - https://doi.org/10.25092/baunfbed.680775
L1  - https://dergipark.org.tr/en/download/article-file/946247
ER  -