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LINEAR ALGEBRA, GEOMETRY AND TRANSFORMATION
Título:
LINEAR ALGEBRA, GEOMETRY AND TRANSFORMATION
Subtítulo:
Autor:
SOLOMON, B
Editorial:
CRC
Año de edición:
2014
ISBN:
978-1-4822-9928-1
Páginas:
474
76,50 €

 

Sinopsis

Features

Provides students with a detailed algebraic and geometric understanding of linear vector functions
Emphasizes both computational and conceptual skills
Uses the Gauss-Jordan algorithm to argue proofs-not just to solve linear systems
Presents the interpretation of matrix/vector multiplication as a linear combination of matrix columns
Focuses on the subspaces of Rn, orthogonality, and diagonalization
Includes exercises in each section, totaling over 500 throughout the book
Summary

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.



Table of Contents

Vectors, Mappings and Linearity
Numeric Vectors
Functions
Mappings and Transformations
Linearity
The Matrix of a Linear Transformation

Solving Linear Systems
The Linear System
The Augmented Matrix and RRE Form
Homogeneous Systems in RRE Form
Inhomogeneous Systems in RRE Form
The Gauss-Jordan Algorithm
Two Mapping Answers

Linear Geometry
Geometric Vectors
Geometric/Numeric Duality
Dot-Product Geometry
Lines, Planes, and Hyperplanes
System Geometry and Row/Column Duality

The Algebra of Matrices
Matrix Operations
Special Matrices
Matrix Inversion
A Logical Digression
The Logic of the Inversion Algorithm
Determinants

Subspaces
Basic Examples and Definitions
Spans and Perps
Nullspace
Column-Space
Perp/Span Conversion
Independence
Basis
Dimension and Rank

Orthogonality
Orthocomplements
Four Subspaces, 16 Questions
Orthonormal Bases
The Gram-Schmidt Algorithm

Linear Transformation
Kernel and Image
The Linear Rank Theorem
Eigenspaces
Eigenvalues and Eigenspaces: Calculation
Eigenvalues and Eigenspaces: Similarity
Diagonalizability and the Spectral Theorem
Singular Value Decomposition

Appendix A: Determinants
Appendix B: Proof of the Spectral Theorem
Appendix C: Lexicon

Index