Elements of Linear Space

Elements of Linear Space is a detailed treatment of the elements of linear spaces, including real spaces with no more than three dimensions and complex n-dimensional spaces. The geometry of conic sections and quadric surfaces is considered, along with algebraic structures, especially vector spaces and transformations. Problems drawn from various branches of geometry are given. Comprised of 12 chapters, this volume begins with an introduction to real Euclidean space, followed by a discussion on linear transformations and matrices. The addition and multiplication of transformations and matrices are given emphasis. Subsequent chapters focus on some properties of determinants and systems of linear equations; special transformations and their matrices; unitary spaces; and some algebraic structures. Quadratic forms and their applications to geometry are also examined, together with linear transformations in general vector spaces. The book concludes with an evaluation of singular values and estimates of proper values of matrices, paying particular attention to linear transformations always on a unitary space of dimension n over the complex field. This book will be of interest to both undergraduate and more advanced students of mathematics.