ABSTRACT
This chapter describes definitions and elementary properties of matrices and determinants. It explores matrices as an example of linear mappings or transformations and outlines spectral analysis of matrices. The concept of matrix norm is analogous to the concept of vector norm. Since matrices and vectors generally occur together, it is desirable that the matrix and vector norms be in consonance with each other. A square matrix has a very special number associated with it. It is called its determinant. The chapter introduces the notion of the determinant of a square matrix. It discusses some more concepts from matrix theory. These are the rank of a matrix, and matrices as linear transformations. Properties of a square matrix can be studied via its eigenvalues and eigenvectors. Eigenvalue is also sometimes referred to as characteristic value, or proper value, or latent value.
