Adjustment Computations, 6th Edition

APPENDIX AINTRODUCTION TO MATRICES

A.1 INTRODUCTION

Matrix algebra provides at least two important advantages: (1) it enables reducing complicated systems of equations to simple expressions that can be visualized and manipulated more easily, and (2) it provides a systematic, mathematical method for solving problems that is well adapted to computers. Problems are frequently encountered in surveying, geodesy, and photogrammetry that require the solution of large systems of equations. This book deals specifically with the analysis and adjustment of redundant observations that must satisfy certain geometric conditions. This frequently results in large equation systems, which when solved according to the least squares method yield most probable estimates for adjusted observations and unknown parameters. As will be demonstrated, matrix methods are particularly well suited for least squares computations, and in this book they are used for analyzing and solving these equation systems.

A.2 DEFINITION OF A MATRIX

A matrix is a set of numbers or symbols arranged in a square or rectangular array of m rows and n columns. The arrangement is such that certain defined mathematical operations can be performed in a systematic and efficient manner. As an example of a matrix representation, consider the following system of three linear equations involving three unknowns:

(A.1)

In Equation ...