Fundamental concept of 3-D matrices

Burhaneddin Izgi; Murat Özkaya

doi:10.1063/1.5047881

Fundamental concept of 3-D matrices

Burhaneddin Izgi^*, Murat Özkaya

^*Corresponding author for this work

Department of Mathematics Engineering

Istanbul Technical University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

Abstract

In this paper, we extend some definitions and properties for the 2-dimensional matrices to the 3-dimensional matrices. We present some basic concepts of the 3-dimensional matrices. Moreover, we introduce the matrix inversion, determinant and condition number vectors for the 3-D matrices. Furthermore, we state and prove Cauchy-Schwarz inequality and some other inequalities related to the 3-dimensional matrix norms. We finally investigate the effects of the third dimension with the new definitions and inequalities by some examples.

Original language	English
Title of host publication	1st International Conference on Mathematical and Related Sciences, ICMRS 2018
Editors	Alper Ekinci, Erhan Set, Mehmet Zeki Sarikaya, Ahmet Ocak Akdemir
Publisher	American Institute of Physics Inc.
ISBN (Electronic)	9780735417076
DOIs	https://doi.org/10.1063/1.5047881
Publication status	Published - 27 Jul 2018
Event	1st International Conference on Mathematical and Related Sciences, ICMRS 2018 - Antalya, Turkey Duration: 30 Apr 2018 → 4 May 2018

Publication series

Name	AIP Conference Proceedings
Volume	1991
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	1st International Conference on Mathematical and Related Sciences, ICMRS 2018
Country/Territory	Turkey
City	Antalya
Period	30/04/18 → 4/05/18

Bibliographical note

Publisher Copyright:
© 2018 Author(s).

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10.1063/1.5047881

Cite this

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title = "Fundamental concept of 3-D matrices",

abstract = "In this paper, we extend some definitions and properties for the 2-dimensional matrices to the 3-dimensional matrices. We present some basic concepts of the 3-dimensional matrices. Moreover, we introduce the matrix inversion, determinant and condition number vectors for the 3-D matrices. Furthermore, we state and prove Cauchy-Schwarz inequality and some other inequalities related to the 3-dimensional matrix norms. We finally investigate the effects of the third dimension with the new definitions and inequalities by some examples.",

author = "Burhaneddin Izgi and Murat {\"O}zkaya",

note = "Publisher Copyright: {\textcopyright} 2018 Author(s).; 1st International Conference on Mathematical and Related Sciences, ICMRS 2018 ; Conference date: 30-04-2018 Through 04-05-2018",

year = "2018",

month = jul,

day = "27",

doi = "10.1063/1.5047881",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

editor = "Alper Ekinci and Erhan Set and Sarikaya, \{Mehmet Zeki\} and Akdemir, \{Ahmet Ocak\}",

booktitle = "1st International Conference on Mathematical and Related Sciences, ICMRS 2018",

}

Izgi, B & Özkaya, M 2018, Fundamental concept of 3-D matrices. in A Ekinci, E Set, MZ Sarikaya & AO Akdemir (eds), 1st International Conference on Mathematical and Related Sciences, ICMRS 2018., 020008, AIP Conference Proceedings, vol. 1991, American Institute of Physics Inc., 1st International Conference on Mathematical and Related Sciences, ICMRS 2018, Antalya, Turkey, 30/04/18. https://doi.org/10.1063/1.5047881

Fundamental concept of 3-D matrices. / Izgi, Burhaneddin; Özkaya, Murat.
1st International Conference on Mathematical and Related Sciences, ICMRS 2018. ed. / Alper Ekinci; Erhan Set; Mehmet Zeki Sarikaya; Ahmet Ocak Akdemir. American Institute of Physics Inc., 2018. 020008 (AIP Conference Proceedings; Vol. 1991).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Fundamental concept of 3-D matrices

AU - Izgi, Burhaneddin

AU - Özkaya, Murat

PY - 2018/7/27

Y1 - 2018/7/27

N2 - In this paper, we extend some definitions and properties for the 2-dimensional matrices to the 3-dimensional matrices. We present some basic concepts of the 3-dimensional matrices. Moreover, we introduce the matrix inversion, determinant and condition number vectors for the 3-D matrices. Furthermore, we state and prove Cauchy-Schwarz inequality and some other inequalities related to the 3-dimensional matrix norms. We finally investigate the effects of the third dimension with the new definitions and inequalities by some examples.

AB - In this paper, we extend some definitions and properties for the 2-dimensional matrices to the 3-dimensional matrices. We present some basic concepts of the 3-dimensional matrices. Moreover, we introduce the matrix inversion, determinant and condition number vectors for the 3-D matrices. Furthermore, we state and prove Cauchy-Schwarz inequality and some other inequalities related to the 3-dimensional matrix norms. We finally investigate the effects of the third dimension with the new definitions and inequalities by some examples.

UR - https://www.scopus.com/pages/publications/85051124117

U2 - 10.1063/1.5047881

DO - 10.1063/1.5047881

M3 - Conference contribution

AN - SCOPUS:85051124117

T3 - AIP Conference Proceedings

BT - 1st International Conference on Mathematical and Related Sciences, ICMRS 2018

A2 - Ekinci, Alper

A2 - Set, Erhan

A2 - Sarikaya, Mehmet Zeki

A2 - Akdemir, Ahmet Ocak

PB - American Institute of Physics Inc.

T2 - 1st International Conference on Mathematical and Related Sciences, ICMRS 2018

Y2 - 30 April 2018 through 4 May 2018

ER -

Fundamental concept of 3-D matrices

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