Linear Algebra Examples C-3: The Eigenvalue Problem and Euclidean Vector Space
The book is a collection of solved problems in linear algebra, this third volume covers the eigenvalue problem and Euclidean vector space. All examples are solved, and the solutions usually consist of step-by-step instructions, and are designed to assist students in methodically solving problems.
Determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space
This book offers a new treatment of the topic, one which is designed to make differential geometry an approachable subject for advanced undergraduates. Professor McCleary considers the historical development of non-Euclidean geometry, placing differential geometry in the context of geometry students will be familiar with from high school. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of a particular surface, the non-Euclidean or hyperbolic plane.
This book is a comprehensive look at geometry – its history, discoverers, and applications - including how it works, and why it works. Along the way are imaginative twists and opposing viewpoints.
Introduction to Fourier Analysis on Euclidean Spaces
The authors present a unified treatment of basic topics that arise in Fourier analysis. Their intention is to illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations, and to motivate the study of harmonic analysis on more general spaces having an analogous structure, e.g., symmetric spaces.