Matrix and Vector Algebra

Summary

Matrices and determinants are very powerful tools in circuit analysis and electromagnetics. Matrices are useful because they enable us to replace an array of many entries as a single symbol and perform operations in a compact symbolic form. This chapter begins by defining a matrix, followed by the algebraic operations and properties. Just like the matrix equality, matrix addition and scalar multiplication are intuitive concepts, for they follow the laws of numbers. The most important special matrices are the diagonal matrix, the identity matrix, and the inverse of a given matrix. An inverse of a square matrix is another matrix of the same size. This new matrix, is perhaps, the most useful matrix in matrix algebra. When discussing Maxwell's equations, a person needs to evaluate a third‐order determinant whose entries are vectors, vector components, and differential operators. The chapter concludes by showing practical EMC‐related applications of matrix algebra.