Abstract
: In this study, the inequalities related to Hadamard product of matrices which has a significant place in linear algebra was compilated. Hadamard product and Kronecker product were introduced and the relations among these products were mentioned. In the main section of study, the inequalities including Hadamard product were emphasized. Finally an equality between the traces of Kronecker product and Hadamard product of two matrices is discovered.
Keywords
Hadamard product Kronecker product Positive definite matrix Positive semidefinite matrix M- Matrix Matrix inequalities
References
- Horn, R.A., The Hadamard Product, in; Proceedings of Symposia in Applied Mathematics, vol. 40, American Mathematical Society Providence, (1990).
- Visick, G., A quantitative version of the Observation that the Hadamard product is a principal submatrix of the Kronecker product, Linear Algebra and Its Applications 304, 45-68, (2000).
- Mond, B. and Pecaric, J.E., Inequalities For The Hadamard Product of Matrices, Siam J. Matrix Anal. Appl., Vol. 19, No. 1, 66-70, Zagreb, (1998).
- Mond, B. and Pecaric, J.E., On Inequalities Involving The Hadamard Product of Matrices, The Electronic Journal of Linear Algebra, Volume 6 56-61, Zagreb, (2000).
- Chen, S., Some determinantal inequalities For Hadamard Product of Matrices, Linear Algebra and Its Applications 368, 99-106, Fuzhou, (2003).
- Gumus, I.H., Yüksek Lisans Tezi, S.Ü. Fen Bilimleri Enstitüsü, Konya (2005).
Abstract
Bu çalışmada lineer cebirde önemli bir yere sahip olan matrislerin Hadamard çarpımı ile ilgili eşitsizlikler derlenmiştir. Hadamard çarpım ve Kronecker çarpım tanıtılıp, bu çarpımlar arasındaki ilişkilerden bahsedilmiştir. Çalışmanın esas kısmında ise Hadamard çarpımı içeren eşitsizlikler üzerinde durulmuştur. Son olarak da iki matrisin Kronecker çarpımlarının izi ile Hadamard çarpımlarının izi arasında bir bağlantı verilmiştir.
Keywords
Hadamard Çarpım Kronecker Çarpım Pozitif tanımlı matris Pozitif yarı tanımlı matris M- Matris Matris eşitsizlikleri
References
- Horn, R.A., The Hadamard Product, in; Proceedings of Symposia in Applied Mathematics, vol. 40, American Mathematical Society Providence, (1990).
- Visick, G., A quantitative version of the Observation that the Hadamard product is a principal submatrix of the Kronecker product, Linear Algebra and Its Applications 304, 45-68, (2000).
- Mond, B. and Pecaric, J.E., Inequalities For The Hadamard Product of Matrices, Siam J. Matrix Anal. Appl., Vol. 19, No. 1, 66-70, Zagreb, (1998).
- Mond, B. and Pecaric, J.E., On Inequalities Involving The Hadamard Product of Matrices, The Electronic Journal of Linear Algebra, Volume 6 56-61, Zagreb, (2000).
- Chen, S., Some determinantal inequalities For Hadamard Product of Matrices, Linear Algebra and Its Applications 368, 99-106, Fuzhou, (2003).
- Gumus, I.H., Yüksek Lisans Tezi, S.Ü. Fen Bilimleri Enstitüsü, Konya (2005).
Details
| Other ID | JA57ZS65UT |
|---|---|
| Authors | |
| Submission Date | December 1, 2011 |
| Publication Date | December 1, 2011 |
| Published in Issue | Year 2011 Volume: 2 Issue: 37 |
Cite
Journal Owner: On behalf of Selçuk University Faculty of Science, Rector Prof. Dr. Hüseyin YILMAZ
Selcuk University Journal of Science Faculty accepts articles in Turkish and English with original results in basic sciences and other applied sciences. The journal may also include compilations containing current innovations.
It was first published in 1981 as "S.Ü. Fen-Edebiyat Fakültesi Dergisi" and was published under this name until 1984 (Number 1-4).
In 1984, its name was changed to "S.Ü. Fen-Edeb. Fak. Fen Dergisi" and it was published under this name as of the 5th issue.
When the Faculty of Letters and Sciences was separated into the Faculty of Science and the Faculty of Letters with the decision of the Council of Ministers numbered 2008/4344 published in the Official Gazette dated 3 December 2008 and numbered 27073, it has been published as "Selcuk University Journal of Science Faculty" between 2009-2025.
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