Research Article
BibTex RIS Cite

Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices

Year 2018, Volume: 9, 50 - 54, 28.12.2018

Abstract

In this article, we discuss some results on the ideals of the real-valued lower triangular Toeplitz matrices (LTTM). Specifically, we provide the basic ring structure, and look at the ideals of LTTM. We provide new findings concerning the ideals of LTTM. 

References

  • Bottcher, A., Grudsky, S.M., Introduction to Large Truncated Toeplitz Matrices, Springer, New York, 1999.
  • Bottcher, A., Grudsky, S.M., Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis, Birkhauser, 2000.
  • Dogan, H., Suarez, L., Matrix Power Computation: Band Toeplitz Structure, International Journal of Computing Algorithm (IJCOA), 6(1)(2017), 55–58.
  • Grenander, U., Szego, G., Toeplitz Forms and Their Applications, University of Calif. Press, Berkeley and Los Angeles, 1958.
  • Kucerovsky, D., Mousavand, K., Sarraf, A., On some properties of Toeplitz matrices, Cogent Mathematics, 3: 1154705(2016).
  • Liu, X., McKee S., Yuan, J.Y., Yuan, Y.X. Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices, Linear Algebra and its Applications, 435(2011), 1157-1170.
  • Vecchio, A. A Bound for the Inverse of a Lower Triangular Toeplitz Matrix, SIAM Journal on Matrix Analysis and Applications, 24(4)(2003), 1167-1174.
  • Ye, K., Lim, L. H., Every matrix is a product of Toeplitz matrices, Foundations of Computational Mathematics, 16(3)(2016), 577–598.
Year 2018, Volume: 9, 50 - 54, 28.12.2018

Abstract

References

  • Bottcher, A., Grudsky, S.M., Introduction to Large Truncated Toeplitz Matrices, Springer, New York, 1999.
  • Bottcher, A., Grudsky, S.M., Toeplitz Matrices, Asymptotic Linear Algebra, and Functional Analysis, Birkhauser, 2000.
  • Dogan, H., Suarez, L., Matrix Power Computation: Band Toeplitz Structure, International Journal of Computing Algorithm (IJCOA), 6(1)(2017), 55–58.
  • Grenander, U., Szego, G., Toeplitz Forms and Their Applications, University of Calif. Press, Berkeley and Los Angeles, 1958.
  • Kucerovsky, D., Mousavand, K., Sarraf, A., On some properties of Toeplitz matrices, Cogent Mathematics, 3: 1154705(2016).
  • Liu, X., McKee S., Yuan, J.Y., Yuan, Y.X. Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices, Linear Algebra and its Applications, 435(2011), 1157-1170.
  • Vecchio, A. A Bound for the Inverse of a Lower Triangular Toeplitz Matrix, SIAM Journal on Matrix Analysis and Applications, 24(4)(2003), 1167-1174.
  • Ye, K., Lim, L. H., Every matrix is a product of Toeplitz matrices, Foundations of Computational Mathematics, 16(3)(2016), 577–598.
There are 8 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Hamide Dogan

Kachmar Khalil This is me

Luis R. Suarez This is me

Publication Date December 28, 2018
Published in Issue Year 2018 Volume: 9

Cite

APA Dogan, H., Khalil, K., & Suarez, L. R. (2018). Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices. Turkish Journal of Mathematics and Computer Science, 9, 50-54.
AMA Dogan H, Khalil K, Suarez LR. Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices. TJMCS. December 2018;9:50-54.
Chicago Dogan, Hamide, Kachmar Khalil, and Luis R. Suarez. “Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices”. Turkish Journal of Mathematics and Computer Science 9, December (December 2018): 50-54.
EndNote Dogan H, Khalil K, Suarez LR (December 1, 2018) Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices. Turkish Journal of Mathematics and Computer Science 9 50–54.
IEEE H. Dogan, K. Khalil, and L. R. Suarez, “Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices”, TJMCS, vol. 9, pp. 50–54, 2018.
ISNAD Dogan, Hamide et al. “Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices”. Turkish Journal of Mathematics and Computer Science 9 (December 2018), 50-54.
JAMA Dogan H, Khalil K, Suarez LR. Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices. TJMCS. 2018;9:50–54.
MLA Dogan, Hamide et al. “Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices”. Turkish Journal of Mathematics and Computer Science, vol. 9, 2018, pp. 50-54.
Vancouver Dogan H, Khalil K, Suarez LR. Some Results on the Ideals of Real-Valued Lower Triangular Toeplitz Matrices. TJMCS. 2018;9:50-4.