Fast change of basis in algebras Hentzel, Irvin Hentzel, Irvin Jacobs, David
dc.contributor.department Mathematics 2018-02-18T23:59:18.000 2020-06-30T05:59:50Z 2020-06-30T05:59:50Z Wed Jan 01 00:00:00 UTC 1992 1992-12-01
dc.description.abstract <p>Given an <em>n</em>-dimensional algebraA represented by a basis<em>B</em> and structure constants, and given a transformation matrix for a new basis<em>C.</em>, we wish to compute the structure constants forA relative to C. There is a straightforward way to solve this problem in<em>O(n</em><sup>5</sup>) arithmetic operations. However given an O(<em>n</em><sub>ω</sub>) matrix multiplication algorithm, we show how to solve the problem in time O(<em>n</em><sub>ω+1</sub>). Using the method of Coppersmith and Winograd, this yields an algorithm of<em>O(n</em><sup>3.376</sup>).</p>
dc.description.comments <p>The final publication is available at Springer via Hentzel, Irvin Roy, and David Pokrass Jacobs. "Fast change of basis in algebras." <em>Applicable Algebra in Engineering, Communication and Computing</em> 3, no. 4 (1992): 257-261. doi:<a href="" target="_blank">10.1007/BF01294835</a>. Posted with permission.</p>
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dc.identifier.articleid 1144
dc.identifier.contextkey 10917130
dc.identifier.s3bucket isulib-bepress-aws-west
dc.identifier.submissionpath math_pubs/139
dc.language.iso en
dc.source.bitstream archive/|||Fri Jan 14 20:03:43 UTC 2022
dc.source.uri 10.1007/BF01294835
dc.subject.disciplines Algebra
dc.subject.disciplines Mathematics
dc.subject.keywords Algebra
dc.subject.keywords Vector space
dc.subject.keywords Transformation matrix
dc.title Fast change of basis in algebras
dc.type article
dc.type.genre article
dspace.entity.type Publication
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relation.isOrgUnitOfPublication 82295b2b-0f85-4929-9659-075c93e82c48
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