Mathematics for Circuits and Filters

2 Bilinear Operators and Matrices

Michael K. Sain

University of Notre Dame

Cheryl B. Schrader

The University of Texas

DOI: 10.1201/9781315214023-2

• 2.1 Introduction
• 2.2 Algebras
• 2.3 Bilinear Operators
• 2.4 Tensor Product
• 2.5 Basis Tensors
• 2.6 Multiple Products
• 2.7 Determinants
• 2.8 Skew Symmetric Products
• 2.9 Solving Linear Equations
• 2.10 Symmetric Products
• 2.11 Summary
• References

2.1 Introduction

The key player in Chapter 1 was the F-vector space V, together with its associated notion of bases, when they exist, and linear operators taking one vector to another. The idea of basis is, of course, quite central to the applications because it permits a vector v in V to be represented by a list of scalars from F. Such lists of ...