Linear Algebra, Geometry and Transformation

1. Auflage 2014
ISBN: 978-1-4822-9928-1
Verlag: CRC Press

Buch, Englisch, 474 Seiten, Format (B × H): 178 mm x 254 mm, Gewicht: 1179 g

Reihe: Textbooks in Mathematics

The Essentials of a First Linear Algebra Course and More

Linear Algebra, Geometry and Transformation provides students with a solid geometric grasp of linear transformations. It stresses the linear case of the inverse function and rank theorems and gives a careful geometric treatment of the spectral theorem.

An Engaging Treatment of the Interplay among Algebra, Geometry, and Mappings

The text starts with basic questions about images and pre-images of mappings, injectivity, surjectivity, and distortion. In the process of answering these questions in the linear setting, the book covers all the standard topics for a first course on linear algebra, including linear systems, vector geometry, matrix algebra, subspaces, independence, dimension, orthogonality, eigenvectors, and diagonalization.

A Smooth Transition to the Conceptual Realm of Higher Mathematics

This book guides students on a journey from computational mathematics to conceptual reasoning. It takes them from simple "identity verification" proofs to constructive and contrapositive arguments. It will prepare them for future studies in algebra, multivariable calculus, and the fields that use them.

Print Versions of this book also include access to the ebook version.

Autoren/Hrsg.

Solomon, Bruce

Fachgebiete

• Mathematik | Informatik Mathematik Algebra
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

Vectors, Mappings, and Linearity. Solving Linear Systems. Linear Geometry. The Algebra of Matrices. Subspaces. Orthogonality. Linear Transformation. Appendices. Index.

Über Autor(innen)

Bruce Solomon is a professor in the Department of Mathematics at Indiana University Bloomington, where he often teaches linear algebra. He has held visiting positions at Stanford University and in Australia, France, and Israel. His research articles explore differential geometry and geometric variational problems. He earned a PhD from Princeton University.