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dc.contributor.authorMarchisella, P
dc.contributor.authorTularam, GA
dc.date.accessioned2017-05-03T14:23:54Z
dc.date.available2017-05-03T14:23:54Z
dc.date.issued2012
dc.date.modified2013-06-17T04:06:30Z
dc.identifier.issn1549-3644
dc.identifier.urihttp://hdl.handle.net/10072/47920
dc.description.abstractProblem statement: Many distinct properties of determinants have been studied and are known, yet a considerable number of properties still need further examination. This study investigates the number of minors (of various orders) and elements of a matrix A contained in the expansion of the general determinant of A, irrespective of the independence, principality and distinctness of such minors and elements. Approach: A mathematical proof based approach is taken. Minors of all orders and elements in the calculations of general determinants of matrices of sizes 2䲬 3䳬 4䴍 and 5䵠respectively, are considered. Results: Two general expressions involving factorial terms are found: the first being equivalent to the number of minors of various orders found in the analysis of the considered matrices (mentioned above) and the second being equivalent to the number of elements found in the same analysis. Proofs are then presented showing that the expressions hold in the general case of a matrix of size n䮮 Conclusion: The results of this study present, with proof, expressions for the total number of minors (of various orders) and elements, respectively, in the general determinant of a matrix of size n䮬 irrespective of the independence, principality and distinctness of such minors and elements. Scope for further theoretical study, with applications in applied mathematics and the physical and computer sciences is also indicated.
dc.description.peerreviewedYes
dc.description.publicationstatusYes
dc.format.extent51914 bytes
dc.format.mimetypeapplication/pdf
dc.languageEnglish
dc.language.isoeng
dc.publisherScience Publications
dc.publisher.placeUnited States
dc.publisher.urihttps://thescipub.com/abstract/jmssp.2012.373.376
dc.relation.ispartofstudentpublicationN
dc.relation.ispartofpagefrom373
dc.relation.ispartofpageto376
dc.relation.ispartofissue3
dc.relation.ispartofjournalJournal of Mathematics and Statistics
dc.relation.ispartofvolume8
dc.rights.retentionY
dc.subject.fieldofresearchPure mathematics
dc.subject.fieldofresearchAlgebra and number theory
dc.subject.fieldofresearchCombinatorics and discrete mathematics (excl. physical combinatorics)
dc.subject.fieldofresearchStatistics
dc.subject.fieldofresearchcode4904
dc.subject.fieldofresearchcode490401
dc.subject.fieldofresearchcode490404
dc.subject.fieldofresearchcode4905
dc.titleNumber of Non-Unique Minors (of Various Orders) and Elements in the Calculation of General Determinants
dc.typeJournal article
dc.type.descriptionC1 - Articles
dc.type.codeC - Journal Articles
gro.facultyArts, Education & Law Group, Queensland Conservatorium
gro.rights.copyright© The Author(s) 2012. The attached file is reproduced here in accordance with the copyright policy of the publisher. For information about this journal please refer to the journal’s website or contact the authors.
gro.date.issued2012
gro.hasfulltextFull Text
gro.griffith.authorMarchisella, Patrick
gro.griffith.authorTularam, Gurudeo A.


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