The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang’s inequalities.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated.
📊
Key Findings & Data:In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated.
💡
Conclusion & Impact:The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang’s inequalities.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Kronecker çarpım · Kronecker toplam · Yarı pozitif tanımlı matrisler
Abstract
In this paper, the trace inequalities involving special products of the positive semidefinite matrices are investigated. The trace inequalities between the Kronecker product and Kronecker sum of two matrices is obtained as in the short note Yang’s inequalities.
Özet
Bu çalışmada, bazı özel matris çarpımları ile ifade edilen yarı pozitif tanımlı çarpım matrislerinin izleri arasındaki eşitsizlikler incelenmiştir. Xin-Min Yang’ın makalesindeki eşitsizliklere bağlı olarak Kronecker çarpım ve toplam matrislerinin izleri arasındaki eşitsizlikler elde edilmiştir.
ÖZEL, M., BULUT, H., ŞAFAK, S., ÇEVEN, Y. (2006). TRACE INEQUALITIES OF POSITIVE SEMIDEFINITE MATRICES. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, Cilt: 8 - Sayı: 2, 107–110. https://ajindex.com/articles/659396
Brewer J.M. (1978): “Kronecker Products and Matrix Calculus in System Theory”, IEEE Transaction on Circuits and Systems, Vol. 25, no. 9, 772-781.
Rao S.S., Mitra S.K. (1971): “Generalized Inverse of Matrices and its Applications”, J.Wiley, New York. Yang X.M. (1995): “A Generalization of a Matrix Trace Inequality”, J. Math. Anal. Appl., 189, 897-900.
Yang Y. (1988): “A Matrix Trace Inequality”, J. Math. Anal. Appl., 133, 573-574.