KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU

Year 2016, , 0 - 0, 26.06.2016

Emre Kişi , Elif Gürer

https://doi.org/10.20854/bujse.258171

Abstract

Xu ve Xu karşılıklı değişmeli iki involutif ve bir tripotent matrisin lineer bileşiminin tripotentliği problemini blok matrislerden yararlanarak çözmüştür [C. Xu., R. Xu, Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute, Linear Algebra Appl. 437 (2012) 2091-2109]. Bu çalışmada ise aynı problem daha genel problemlerin çözümlerinde kullanılabilir olan farklı bir yöntem ile çözülmüştür.

Keywords

tripotent matris, involutif matris; lineer bileşim

References

• S.L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press Inc., New York, 1995.
• O.M. Baksalary, Idempotency of linear combinations of three idempotent matrices, two of which are disjoint, Linear Algebra Appl. 388 (2004) 67-78.
• J.K. Baksalary, O.M. Baksalary, Idempotency of linear combinations of two idempotent matrices, Linear Algebra Appl. 321 (2000) 3-7.
• J.K. Baksalary, O.M. Baksalary, When is a linear combination of two idempotent matrices the group involutory matrix?, Linear and Multilinear Algebra 54(6) (2006) 429-435.
• J.K. Baksalary, O.M. Baksalary, H. Özdemir, A note on linear combinations of commuting tripotent matrices, Linear Algebra Appl. 388 (2004) 45-51.
• J.K. Baksalary, O.M. Baksalary, G.P.H. Styan, Idempotency of linear combinations of an idempotent matrix and a tripotent matrix, Linear Algebra Appl. 354 (2002) 21-34.
• O.M. Baksalary, J. Benitez, Idempotency of linear combinations of three idempotent matrices, two of which are commuting, Linear Algebra Appl. 424 (2007) 320-337.
• B. Baldessari, The distribution of a quadratic form of normal random variables, Ann. Math. Statist. 38 (1967) 1700–1704.
• J. Benitez, N. Thome, Idempotency of linear combinations of an idempotent matrix and a t-potent matrix that commute, Linear Algebra Appl. 403 (2005) 414-418.
• J. Benitez, N. Thome, Idempotency of linear combinations of an idempotent matrix and a t-potent matrix that do not commute, Linear and Multilinear Algebra 56 (2008) 679-687.
• D.S. Bernstein, Matrix Mathematics, Theory, Facts, and Formulas, 2nd ed., Princeton U.P., New Jersey, 2009.
• C. Coll, N. Thome, Oblique projectors and group involutory matrices, Appl. Math. Comput. 140 (2003) 517-522.
• C.Y. Deng, D.S. Cvetković-Ilić, Y. Wei, Properties of the combinations of commutative idempotents, Linear Algebra Appl. 436 (2012) 202–221.
• N.J. Higham, Functions of Matrices, SIAM, Philadelphia, 2008.
• R.A Horn. and C.R Johnson, Matrix Analysis 2nd ed., Cambridge U.P., Cambridge, 2013.
• E. Kişi, Corrigendum to “Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute” [Linear Algebra Appl. 437 (9) (2012) 2091–2109], Linear Algebra Appl. 477 (2015) 211–212.
• H. Özdemir, M. Sarduvan., A.Y. Özban, N. Güler, On idempotency and tripotency of linear combinations of two commuting tripotent matrices, Appl Math. Comput. 207 (2009) 197-201.
• M. Sarduvan, H. Özdemir, On linear combinations of two tripotent, idempotent, and involutive matrices, Appl Math. Comput. 200 (2008) 401-406.
• G.A.F. Seber. Matrix Handbook for Statisticians. Wiley, New Jersey, 2007.
• M. Tošic, On some linear combinations of commuting involutive and idempotent matrices, Appl. Math. Comput. 233 (2014) 103–108.
• Y.Wu,K-Potentmatrices-construction and applications in digital image encryption, in: Recent Advances in AppliedMathematics, AMERICAN-MATH’10 Proceedings of the 2010 American Conference on Applied mathematics, USA, 2010, pp. 455–460.
• C. Xu, On the idempotency, involution and nilpotency of a linear combination of two matrices, Linear and Multilinear Algebra 63 (2015) 1664-1677.
• C. Xu., R. Xu, Tripotency of a linear combination of two involutory matrices and a tripotent matrix that mutually commute, Linear Algebra Appl. 437 (2012) 2091-2109.