Mathematics for Circuits and Filters

1 Linear Operators and Matrices

Cheryl B. Schrader

The University of Texas

Michael K. Sain

University of Notre Dame

DOI: 10.1201/9781315214023-1

• 1.1 Introduction
• 1.2 Vector Spaces Over Fields
• 1.3 Linear Operators and Matrix Representations
• 1.4 Matrix Operations
• 1.5 Determinant, Inverse, and Rank
• 1.6 Basis Transformations
• 1.7 Characteristics: Eigenvalues, Eigenvectors, and Singular Values
• 1.8 On Linear Systems
• References

1.1 Introduction

It is only after the engineer masters linear concepts-linear models, and circuit and filter theory-that the possibility of tackling nonlinear ideas becomes achievable. Students frequently encounter linear methodologies, and bits and pieces of mathematics that aid in problem solution are ...