Introduction to Matrices
Fletcher Dunn, Ian Parberry · 2011
This chapter introduces the theory and application of matrices. It explains how to interpret the properties and operations geometrically. The chapter discusses some of the basic properties and operations of matrices strictly from a mathematical perspective. It presents matrices from a purely mathematical perspective. Matrices may have any positive number of rows and columns, including one. The matrices that arise in practice are not boxes full of random numbers; rather, they express organized relationships and have a great deal of structure. The chapter also introduces the concept of matrix dimension and describes some matrix notation and traces square matrices. It explores vectors as matrices, also describes matrix transposition and investigates how to multiply a matrix by a scalar. The chapter also explains how to multiply a matrix by another matrix, shows how to multiply a vector by a matrix and aims to compares and contrasts matrices for row and column vectors.