{"title":"On the Determinant-like Function and the Vector Determinant","authors":"Abhimanyu Pallavi Sudhir","doi":"10.1007/s00006-014-0455-3","DOIUrl":null,"url":null,"abstract":"<div><p>A generalisation of the determinant to rectangular matrices, known as the determinant-like function, has its magnitude defined previously. In this paper, we show that the determinant-like function is a rotation of the vector determinant.We further propose that this rotation is an identity transformation and thus the determinant-like function is in fact the same as the vector determinant. From this, we derive some properties of the determinant-like function.</p></div>","PeriodicalId":7330,"journal":{"name":"Advances in Applied Clifford Algebras","volume":"24 3","pages":"805 - 807"},"PeriodicalIF":1.2000,"publicationDate":"2014-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00006-014-0455-3","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Applied Clifford Algebras","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00006-014-0455-3","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 1
Abstract
A generalisation of the determinant to rectangular matrices, known as the determinant-like function, has its magnitude defined previously. In this paper, we show that the determinant-like function is a rotation of the vector determinant.We further propose that this rotation is an identity transformation and thus the determinant-like function is in fact the same as the vector determinant. From this, we derive some properties of the determinant-like function.
期刊介绍：
Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.
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