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How to Fill the Sample Null Space

James G. Sanderson and Stuart L. Pimm

in Patterns In Nature: The Analysis of Species Co-Occurrences

Published in print:
2015
Published Online:
May 2016
ISBN:
9780226292724
eISBN:
9780226292861
Item type:
chapter
Publisher:
University of Chicago Press
DOI:
10.7208/chicago/9780226292861.003.0005
Subject:
Biology, Biodiversity / Conservation Biology

Chapter 5 describes how sample random, or null, matrices are created so that each is representative of the actual, or observed, incidence matrix. Four different methods, or algorithms, to create each ... More


Matrix Properties, Fundamental Spaces, Orthogonality

Gidon Eshel

in Spatiotemporal Data Analysis

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691128917
eISBN:
9781400840632
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691128917.003.0003
Subject:
Environmental Science, Environmental Studies

This chapter provides an introduction to linear algebra. Topics covered include vector spaces, matrix rank, fundamental spaces associated with A ɛ ℝM×N, and Gram–Schmidt orthogonalization. In ... More


The Semi-group on

Charles L. Epstein and Rafe1 Mazzeo

in Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Published in print:
2013
Published Online:
October 2017
ISBN:
9780691157122
eISBN:
9781400846108
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691157122.003.0012
Subject:
Mathematics, Probability / Statistics

This chapter deals with the semi-group on the space Β‎⁰(P). It first describes the boundary behavior of elements of the adjoint operator at points in the interiors of hypersurface boundary components ... More


The solve phase

I. S. Duff, A. M. Erisman, and J. K. Reid

in Direct Methods for Sparse Matrices

Published in print:
2017
Published Online:
April 2017
ISBN:
9780198508380
eISBN:
9780191746420
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198508380.003.0014
Subject:
Mathematics, Numerical Analysis

We examine the SOLVE phase in the direct solution of sparse systems. Here we assume that the factors have been computed and we study the efficient use of these to determine the solution through ... More


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