Alternative characterizations of some linear combinations of an idempotent matrix and a tripotent matrix that commute

Tuğba Petik, Burak Tufan Gökmen

Öz


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.

Tam Metin:

PDF

Referanslar


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).

Baksalary, J.K. and Baksalary, O.M., Idempotency of linear combinations of two idempotent matrices, Linear Algebra and its Applications, 321, 1, 3-7, (2000).

Baksalary, J.K., Baksalary, O.M., and Styan, G.P.H., Idempotency of linear combinations of an idempotent matrix and a tripotent matrix, Linear Algebra and its Applications, 354, 21-34, (2002).

Özdemir, H. and Özban, A.Y., On idempotency of linear combinations of idempotent matrices, Applied Mathematics and Computation, 159, 439-448, (2004).

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).

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).

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).

Sarduvan, M. and Özdemir, H., On linear combinations of two tripotent, idempotent and involutive matrices, Applied Mathematics and Computation, 200, 401-406, (2008).

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).

Uç, M., Petik, T., and Özdemir, H., The generalized quadraticity of linear combinations of two commuting quadratic matrices, Linear and Multilinear Algebra, 64, 9, 1696-1715, (2016).

Baksalary, O.M., Idempotency of linear combinations of three idempotent matrices, two of which are disjoint, Linear Algebra and its Applications, 388, 67-78, (2004).

Baksalary O.M and Benítez, J., Idempotency of linear combinations of three idempotent matrices, two of which are commuting, Linear Algebra and its Applications, 424, 320-337, (2007).

Petik, T., Uç, M., Özdemir, H., Generalized quadraticity of linear combination of two generalized quadratic matrices, Linear and Multilinear Algebra, 63, 2430-2439, (2015).


Refback'ler

  • Şu halde refbacks yoktur.


Telif Hakkı (c) 2020 Tuğba Petik, Burak Tufan Gökmen

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.