Name: Fundamentals of Linear Algebra
Price: 69.99 USD
Availability: InStock
ISBN: 9781138590502

Fundamentals of Linear Algebra, 1st Edition, by J.S. Chahal, is a textbook published by Chapman & Hall that presents core principles of the discipline in less than 250 pages. The work develops foundational theory alongside practical applications in an effort to raise expectations and outcomes.

The volume surveys core subjects including matrix algebra, vector spaces, linear maps, and determinants. It also examines diagonalization, inner product spaces, and linear algebra over complex numbers.

A central feature of the text is its presentation of linear algebra over arbitrary fields. Rather than restricting proofs to finite-dimensional settings, the book proves the existence of a basis for any given vector space and incorporates non-trivial examples addressing real-world problems.

Table of Contents

Chapter 1: Preliminaries
- • What is Linear Algebra?
- • Rudimentary Set Theory
- • Cartesian Products
- • Relations
- • Concept of a Function
- • Composite Functions
- • Fields of Scalars
- • Techniques for Proving Theorems
Chapter 2: Matrix Algebra
- • Matrix Operations
- • Geometric Meaning of a Matrix Equation
- • Systems of Linear Equation
- • Inverse of a Matrix
- • The Equation Ax=b
- • Basic Applications
Chapter 3: Vector Spaces
- • The Concept of a Vector Space
- • Subspaces
- • The Dimension of a Vector Space
- • Linear Independence
- • Application of Knowing dim (V)
- • Coordinates
- • Rank of a Matrix
Chapter 4: Linear Maps
- • Linear Maps
- • Properties of Linear Maps
- • Matrix of a Linear Map
- • Matrix Algebra and Algebra of Linear Maps
- • Linear Functionals and Duality
- • Equivalence and Similarity
- • Application to Higher Order Differential Equations
Chapter 5: Determinants
- • Motivation
- • Properties of Determinants
- • Existence and Uniqueness of Determinant
- • Computational Definition of Determinant
- • Evaluation of Determinants
- • Adjoint and Cramer's Rule
Chapter 6: Diagonalization
- • Motivation
- • Eigenvalues and Eigenvectors
- • Cayley-Hamilton Theorem
Chapter 7: Inner Product Spaces
- • Inner Product
- • Fourier Series
- • Orthogonal and Orthonormal Sets
- • Gram-Schmidt Process
- • Orthogonal Projections on Subspaces
Chapter 8: Linear Algebra over Complex Numbers
- • Algebra of Complex Numbers
- • Diagonalization of Matrices with Complex Eigenvalues
- • Matrices over Complex Numbers
Chapter 9: Orthonormal Diagonalization
- • Motivational Introduction
- • Matrix Representation of a Quadratic Form
- • Spectral Decompostion
- • Constrained Optimization-Extrema of Spectrum
- • Singular Value Decomposition (SVD)
Chapter 10: Selected Applications of Linear Algebra
- • System of First Order Linear Differential Equations
- • Multivariable Calculus
- • Special Theory of Relativity
- • Cryptography
- • Solving Famous Problems from Greek Geometry

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