# Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements, Volume v

## 1st Edition

**Authors:**S. Twomey

**Print ISBN:**9780444415479

**eBook ISBN:**9781483289564

**Imprint:**Elsevier Science

**Published Date:**1st February 1977

## Description

Developments in Geomathematics, 3: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements focuses on the application of the mathematics of inversion in remote sensing and indirect measurements, including vectors and matrices, eigenvalues and eigenvectors, and integral equations.

The publication first examines simple problems involving inversion, theory of large linear systems, and physical and geometric aspects of vectors and matrices. Discussions focus on geometrical view of matrix operations, eigenvalues and eigenvectors, matrix products, inverse of a matrix, transposition and rules for product inversion, and algebraic elimination. The manuscript then tackles the algebraic and geometric aspects of functions and function space and linear inversion methods, as well as the algebraic and geometric nature of constrained linear inversion, least squares solution, approximation by sums of functions, and integral equations. The text examines information content of indirect sensing measurements, further inversion techniques, and linear inversion methods.

The publication is a valuable reference for researchers interested in the application of the mathematics of inversion in remote sensing and indirect measurements.

## Table of Contents

Preface

List of Frequently Used Symbols and their Meanings

Chapter 1. Introduction

1.1. Mathematical Description of the Response of a Real Physical Remote Sensing System

1.2. Examples of Real Inversion Problems

Bibliography

Chapter 2. Simple Problems Involving Inversion

2.1. Algebraic Elimination

2.2. Quadrature, The Reduction of Integral Equations to Systems of Linear Equations

Bibliography

Chapter 3. Theory of Large Linear Systems

3.1. Matrix-Vector Algebra

3.2. Matrix Products

3.3. Inverse of a Matrix

3.4. Transposition and Rules for Product Inversion

Bibliography

Chapter 4. Physical and Geometric Aspects of Vectors and Matrices

4.1. Geometric Vectors

4.2. Norms, Length and Distance

4.3. Orthogonality

4.4. Geometrical View of Matrix Operations

4.5. Eigenvalues and Eigenvectors

4.6. Quadratic Forms, Eigenvalues and Eigenvectors

Bibliography

Chapter 5. Algebraic and Geometric Aspects of Functions and Function Space

5.1. Orthogonality, Norms and Length

5.2. Other Kinds of Orthogonality

5.3. Approximation by Sums of Functions

5.4. Integral Equations

5.5. The Fourier Transform and Fourier Series

5.6. Spectral Form of the Fundamental Integral Equation of Inversion

Bibliography

Chapter 6. Linear Inversion Methods

6.1. Quadrature Inversion

6.2. Least Squares Solution

6.3. Constrained Linear Inversion

6.4. Sample Applications of Constrained Linear Inversion

6.5. Algebraic Nature of Constrained Linear Inversion

6.6. Geometric Nature of Constrained Linear Inversion

Bib

## Details

- Language:
- English

- Copyright:
- © Elsevier Science 1977

- Published:
- 1st February 1977

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9781483289564

- Hardcover ISBN:
- 9780444415479

## About the Author

### S. Twomey

## Reviews

Developments in Geomathematics, 3: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurements focuses on the application of the mathematics of inversion in remote sensing and indirect measurements, including vectors and matrices, eigenvalues and eigenvectors, and integral equations. The publication first examines simple problems involving inversion, theory of large linear systems, and physical and geometric aspects of vectors and matrices. Discussions focus on geometrical view of matrix operations, eigenvalues and eigenvectors, matrix products, inverse of a matrix, transposition and rules for product inversion, and algebraic elimination. The manuscript then tackles the algebraic and geometric aspects of functions and function space and linear inversion methods, as well as the algebraic and geometric nature of constrained linear inversion, least squares solution, approximation by sums of functions, and integral equations. The text examines information content of indirect sensing measurements, further inversion techniques, and linear inversion methods. The publication is a valuable reference for researchers interested in the application of the mathematics of inversion in remote sensing and indirect measurements.