Vectors and Matrices
David O. Yevick, Hannah G. Yevick · 2014
Linear equation systems are conveniently described with rectangular arrays of numeric values termed matrices. As algebraic operations on matrices act on groups of elements, their properties are restricted compared to manipulations of single values. This chapter briefly talks about the vectors and matrices. A vector possesses both a scalar (numeric) magnitude that is independent of the coordinate system and a direction that is described differently in different coordinate systems. For example, the displacement vector can be represented by an arrow directed from the initial to the final spatial position where the magnitude of the displacement, the scalar distance, equals the length of the arrow. The chapter also discusses the cross and outer products, vector identities, rotations and orthogonal matrices, groups and matrix generators, and eigenvalues and eigenvectors. The eigenvalues of Hermitian and anti-Hermitian matrices are purely real and imaginary, respectively. Finally, the chapter discusses similarity transformations in detail.