Abstract
Bu çalışmada öncelikle nn× tipindeki bir kompleks A matrisinin singüler değerleri için iz ve determinant kullanılarak sınırlar elde edilmiştir. Aynı zamanda satır (sütun) Euclidean normu kullanılarak singüler değerlerinin çarpımı için sınırlar elde edilmiştir. Son olarak ise () n ji n hjig T 0, 1 = −+ = Cauchy-Toeplitz matrisi ve () n ji n hjig H 0, 1 = ++ = Cauchy-Hankel matrisinin Euclidean ve spektral normları için bir alt sınır bulunmuştur.
References
- [1] Güngör A. D., Singüler ve Norm Değerleri İçin Sınırlar, Doktora Tezi, Selçuk Üniversitesi, Konya, (2004).
- [2] Marshall, A. W., Olkin, I., Inequalities, Theory of Majorization and its Applications, Academic, New York, (1979).
- [3] Merikoski, J. K., Virtanen, A., Bounds for eigenvalues using the trace and determinant, Linear Algebra and its Applications 264, 101-108(1997) .
- [4] Rojo Oscar, Further bounds for the smallest singular values and the spectral condition numbers, Computers and Mathematics with Applications, Vol. 38, No. 7-8 : 215-228 (1999).
- [5] Wang B., Zhang F., Some Inequalities for the Eigenvalues of the Product of Positive Semidefinite Hermitian Matrices, Linear Algebra and Its Applications 160: 113-118 (1992)
Abstract
In this study, firstly we have obtained bounds for singular values of a complex matrix A of order n× n using the trace and determinant. In addition, we have obtained bounds for products of singular values using row (column) Frobenius (or Euclidean) norms and determinant. Consequently, we have found lower bounds for the Euclidean norms and spectral norms of Cauchy-Toeplitz matrix ( ) n i j n g i j h T , 0 1 = + − = and Cauchy-Hankel matrix ( ) n i j n g i j h H , 0 1 = + + = .
References
- [1] Güngör A. D., Singüler ve Norm Değerleri İçin Sınırlar, Doktora Tezi, Selçuk Üniversitesi, Konya, (2004).
- [2] Marshall, A. W., Olkin, I., Inequalities, Theory of Majorization and its Applications, Academic, New York, (1979).
- [3] Merikoski, J. K., Virtanen, A., Bounds for eigenvalues using the trace and determinant, Linear Algebra and its Applications 264, 101-108(1997) .
- [4] Rojo Oscar, Further bounds for the smallest singular values and the spectral condition numbers, Computers and Mathematics with Applications, Vol. 38, No. 7-8 : 215-228 (1999).
- [5] Wang B., Zhang F., Some Inequalities for the Eigenvalues of the Product of Positive Semidefinite Hermitian Matrices, Linear Algebra and Its Applications 160: 113-118 (1992)
Details
| Other ID | JA58MC89AP |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | December 1, 2005 |
| Submission Date | December 1, 2005 |
| Published in Issue | Year 2005 Volume: 1 Issue: 25 |
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" since 2009.
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