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On the Hadamard Product of Matrices

Year 2011, Volume: 2 Issue: 37, 9 - 14, 01.12.2011

İ. Halil Gümüş Necati Taşkara

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).

Matrislerin Hadamard Çarpımı Üzerine

Year 2011, Volume: 2 Issue: 37, 9 - 14, 01.12.2011

İ. Halil Gümüş Necati Taşkara

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).
There are 6 citations in total.

Details

Other ID JA57ZS65UT
Journal Section Research Articles
Authors

İ. Halil Gümüş

Necati Taşkara This is me

Publication Date December 1, 2011
Submission Date December 1, 2011
Published in Issue Year 2011 Volume: 2 Issue: 37

Cite

APA Gümüş, İ. H., & Taşkara, N. (2011). Matrislerin Hadamard Çarpımı Üzerine. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, 2(37), 9-14.
AMA Gümüş İH, Taşkara N. Matrislerin Hadamard Çarpımı Üzerine. sufefd. December 2011;2(37):9-14.
Chicago Gümüş, İ. Halil, and Necati Taşkara. “Matrislerin Hadamard Çarpımı Üzerine”. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi 2, no. 37 (December 2011): 9-14.
EndNote Gümüş İH, Taşkara N (December 1, 2011) Matrislerin Hadamard Çarpımı Üzerine. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi 2 37 9–14.
IEEE İ. H. Gümüş and N. Taşkara, “Matrislerin Hadamard Çarpımı Üzerine”, sufefd, vol. 2, no. 37, pp. 9–14, 2011.
ISNAD Gümüş, İ. Halil - Taşkara, Necati. “Matrislerin Hadamard Çarpımı Üzerine”. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi 2/37 (December 2011), 9-14.
JAMA Gümüş İH, Taşkara N. Matrislerin Hadamard Çarpımı Üzerine. sufefd. 2011;2:9–14.
MLA Gümüş, İ. Halil and Necati Taşkara. “Matrislerin Hadamard Çarpımı Üzerine”. Selçuk Üniversitesi Fen Fakültesi Fen Dergisi, vol. 2, no. 37, 2011, pp. 9-14.
Vancouver Gümüş İH, Taşkara N. Matrislerin Hadamard Çarpımı Üzerine. sufefd. 2011;2(37):9-14.

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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).
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