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OverviewPlease note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! Given m and n and r < min(m, n), the determinantal variety Y r is the set of all m Ao n matrices (over a field k) with rank ae r. This is naturally an algebraic variety as the condition that a matrix have rank ae r is given by the vanishing of all of its (r + 1) Ao (r + 1) minors. Considering the generic m Ao n matrix whose entries are algebraically independent variables x i,j, these minors are polynomials of degree r + 1. The ideal of k[x i,j] generated by these polynomials is a determinantal ideal. Since the equations defining minors are homogeneous, one can consider Y r either as an affine variety in mn-dimensional affine space, or as a projective variety in (mn ae' 1)-dimensional projective space. Full Product DetailsAuthor: Lambert M. Surhone , Miriam T. Timpledon , Susan F. MarsekenPublisher: VDM Publishing House Imprint: VDM Publishing House Dimensions: Width: 22.90cm , Height: 0.50cm , Length: 15.20cm Weight: 0.136kg ISBN: 9786131194870ISBN 10: 6131194874 Pages: 84 Publication Date: 12 August 2010 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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