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

Year 2016, , 0 - 0, 26.06.2016
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.

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.
Year 2016, , 0 - 0, 26.06.2016
https://doi.org/10.20854/bujse.258171

Abstract

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.
There are 23 citations in total.

Details

Journal Section Articles
Authors

Emre Kişi

Elif Gürer This is me

Publication Date June 26, 2016
Published in Issue Year 2016

Cite

APA Kişi, E., & Gürer, E. (2016). KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 9(1). https://doi.org/10.20854/bujse.258171
AMA Kişi E, Gürer E. KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU. BUJSE. June 2016;9(1). doi:10.20854/bujse.258171
Chicago Kişi, Emre, and Elif Gürer. “KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 9, no. 1 (June 2016). https://doi.org/10.20854/bujse.258171.
EndNote Kişi E, Gürer E (June 1, 2016) KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 9 1
IEEE E. Kişi and E. Gürer, “KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU”, BUJSE, vol. 9, no. 1, 2016, doi: 10.20854/bujse.258171.
ISNAD Kişi, Emre - Gürer, Elif. “KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 9/1 (June 2016). https://doi.org/10.20854/bujse.258171.
JAMA Kişi E, Gürer E. KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU. BUJSE. 2016;9. doi:10.20854/bujse.258171.
MLA Kişi, Emre and Elif Gürer. “KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 9, no. 1, 2016, doi:10.20854/bujse.258171.
Vancouver Kişi E, Gürer E. KARŞILIKLI DEĞİŞMELİ İKİ İNVOLUTİF VE BİR TRİPOTENT MATRİSİN LİNEER BİLEŞİMİNİN TRİPOTENTLİĞİNİN BİR ALTERNATİF KARAKTERİZASYONU. BUJSE. 2016;9(1).