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Faal, H., Bayat, M. (2018). A New Method for Computing Determinants By Reducing The Orders By Two. Caspian Journal of Mathematical Sciences (CJMS), 7(1), 16-24. doi: 10.22080/cjms.2017.12082.1315
Hossein Teimoori Faal; Morteza Bayat. "A New Method for Computing Determinants By Reducing The Orders By Two". Caspian Journal of Mathematical Sciences (CJMS), 7, 1, 2018, 16-24. doi: 10.22080/cjms.2017.12082.1315
Faal, H., Bayat, M. (2018). 'A New Method for Computing Determinants By Reducing The Orders By Two', Caspian Journal of Mathematical Sciences (CJMS), 7(1), pp. 16-24. doi: 10.22080/cjms.2017.12082.1315
Faal, H., Bayat, M. A New Method for Computing Determinants By Reducing The Orders By Two. Caspian Journal of Mathematical Sciences (CJMS), 2018; 7(1): 16-24. doi: 10.22080/cjms.2017.12082.1315

A New Method for Computing Determinants By Reducing The Orders By Two

Article 2, Volume 7, Issue 1, Winter and Spring 2018, Page 16-24  XML PDF (101 K)
Document Type: Research articles
DOI: 10.22080/cjms.2017.12082.1315
Authors
Hossein Teimoori Faal 1; Morteza Bayat2
1Department of Mathematics and Computer Science, Allameh Tabatabai University of Tehran
2‎Department of Mathematics, Zanjan Branch‎, ‎Islamic Azad University‎, ‎Zanjan‎, ‎Iran
Abstract
In this paper we will present a new method to calculate determinants of square matrices. The method is based on the Chio-Dodgson's condensation formula and our approach automatically affects in reducing the order of determinants by two. Also, using the Chio's condensation method we present an inductive proof of Dodgson's determinantal identity.
Keywords
Chio's condensation Method; Dodgson's Condensation Method; determinants; determinantal identity; Laplace expansion
Article Title [Persian]
یک روش جدید برای محاسبه ی دترمینان ها با کاهش مرتبه ها به اندازه ی دو
Abstract [Persian]
در این مقاله ما یک روش جدید برای محاسبه ی دترمینان ها ی ماتریس مربعی ارائه می دهیم. این روش بر اساس فرمول چگالش چیو بوده و راهکار ما به طور خودکار در کاهش مرتبه ی دترمینان ها به اندازه ی دو اثر دارد. همچنین، با استفاده از روش چگالش چیو ما یک اثبات استقرایی از اتحاد دترمینانی داجسون ارائه می دهیم.
Keywords [Persian]
روش چگالش چیو، روش چگالش داجسون، دترمینان ها، اتحاد دترمینانی، بسط لاپلاس
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