Linear Algebra I: Basic Concepts eBook

This is the first volume of the two-volume book on linear algebra, in the University of Tokyo (UTokyo) Engineering Course.

The objective of this volume is to present, from the engineering viewpoint, the standard mathematical results in linear algebra such as those on systems of equations and eigenvalue problems. In addition to giving mathematical theorems and formulas, it explains how the mathematical concepts such as rank, eigenvalues, and singular values are linked to engineering applications and numerical computations.

In particular, the following four aspects are emphasized.

Contents:

• Preface
• Matrices
• Determinants
• Elementary Transformations and Elimination
• Rank
• Systems of Linear Equations
• Eigenvalues
• Quadratic Forms
• Singular Values and the Method of Least Squares
• Vector Spaces
• Bibliography
• Index

Readership: Undergraduate students majoring in engineering and other mathematical sciences.

Key Features:

• This book takes the approach of developing theories through concrete matrix representations rather than through abstract concepts
• It aims at self-contained presentations of mathematical arguments, so that the reader can follow them without referring to other sources
• Serious effort has been made to relate mathematical concepts and theorems to engineering applications, although no attempt has been made to provide actual case studies that demonstrate the use of linear algebra