## 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