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The Fundamental Theorem of Linear Algebra

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/9780691128917.003.0010
Subject:
Environmental Science, Environmental Studies

This chapter summarizes pictorially some of the linear algebraic foundations discussed thus far by revisiting the fundamental theorem of linear algebra, the unifying view of matrices, vectors, and ... More


GROUP ORBITALLY CONSTRAINED APPROXIMATION

Moody T. Chu and Gene H. Golub

in Inverse Eigenvalue Problems: Theory, Algorithms, and Applications

Published in print:
2005
Published Online:
September 2007
ISBN:
9780198566649
eISBN:
9780191718021
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780198566649.003.0009
Subject:
Mathematics, Applied Mathematics

Group actions together with properly formulated objective functions can offer a channel to tackle various classical or new and challenging problems rising from applied linear algebra. This chapter ... 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


Regression and Least Squares

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/9780691128917.003.0009
Subject:
Environmental Science, Environmental Studies

This chapter focuses on linear regression, the process of identifying the unique model that best explains a set of observed data among a specified class of general models. Regression thus occupies a ... More


Notation and Basic Operations

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/9780691128917.003.0002
Subject:
Environmental Science, Environmental Studies

This chapter introduces some of the basic players of the algebraic drama about to unfold, and the uniform notations used in this book. While Chapter 3 is a more formal introduction to linear algebra, ... More


The Gray World of Practical Data Analysis: An Introduction to Part 2

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/9780691128917.003.0006
Subject:
Environmental Science, Environmental Studies

This chapter provides an overview of the second part of the book. This part is the crux of the matter: how to analyze actual data. While this part builds on Part 1, especially on linear algebra ... More


Spatiotemporal Data Analysis

Gidon Eshel

Published in print:
2011
Published Online:
October 2017
ISBN:
9780691128917
eISBN:
9781400840632
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691128917.001.0001
Subject:
Environmental Science, Environmental Studies

A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm’s mutation into a deadly twister? Avian flu cases are reported in China. How ... More


Topics in Quaternion Linear Algebra

Leiba Rodman

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161853
eISBN:
9781400852741
Item type:
book
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161853.001.0001
Subject:
Mathematics, Algebra

Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied ... More


Matrix algorithms and graph partitioning: A discussion of network algorithms that use matrix and linear algebra methods, including algorithms for partitioning network nodes into groups

M. E. J. Newman

in Networks: An Introduction

Published in print:
2010
Published Online:
September 2010
ISBN:
9780199206650
eISBN:
9780191594175
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199206650.003.0011
Subject:
Physics, Theoretical, Computational, and Statistical Physics

The preceding chapter discussed a variety of computer algorithms for calculating quantities of interest on networks, including degrees, centralities, shortest paths, and connectivity. This chapter ... More


Introduction

Leiba Rodman

in Topics in Quaternion Linear Algebra

Published in print:
2014
Published Online:
October 2017
ISBN:
9780691161853
eISBN:
9781400852741
Item type:
chapter
Publisher:
Princeton University Press
DOI:
10.23943/princeton/9780691161853.003.0001
Subject:
Mathematics, Algebra

This chapter provides a brief overview of this volume, showing that this book can be used for a variety of ways and can be used to assist the reader toward a better understanding of quaternion linear ... More


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