Power Electronic Systems

Appendix A Introduction to Linear Algebra

A matrix is a rectangular array of variables, mathematical expressions, or simply numbers. Commonly, a matrix is written as

A=[a11a12…a1na21a22…a2n⋮⋮⋱⋮am1am2⋯amn]⁢(A.1)

The size of the matrix, with m rows and n columns, is called an m-by-n (or m × n) matrix, where m and n are called its dimensions.

A matrix with one row [a (1 × n) matrix] is called a row vector and a matrix with one column [an (m × 1) matrix] is called a column vector. Any isolated row or column of a matrix is a row or column vector, obtained by removing all other rows or columns, respectively, from the matrix.

A.1 Square Matrices

A square matrix is a matrix with m = n, that is, the same number of rows and columns. An n-by-n matrix ...