This book is
meant to provide an introduction to vectors, matrices, and least squares
methods, basic topics in applied linear algebra. Our goal is to give the
beginning student, with little or no prior exposure to linear algebra, a good
grounding in the basic ideas, as well as an appreciation for how they are used
in many applications, including data fitting, machine learning and artificial
intelligence, tomography, image processing, finance, and automatic control
systems. Topics covered includes: Vectors, Norm and distance, Clustering,
Matrices, Linear equations, Matrix multiplication, Linear dynamical systems,
Least squares, Multi-objective least squares, Constrained least squares.
The contents of this book include: Systems of Equations,
Matrices, Determinants, Linear Transformations, Complex Numbers, Spectral
Theory, Some Curvilinear Coordinate Systems, Vector Spaces.
This
note explains the following topics: Eigenvalues and Eigenvectors, The
spectral theorem, Tensor Products, Fourier Analysis and Quadrtic Reciprocity.
The purpose with
these notes is to introduce students to the concept of proof in linear algebra
in a gentle manner. Topics covered includes: Matrices and Matrix Operations,
Linear Equations, Vector Spaces, Linear Transformations, Determinants, Eigenvalues and Eigenvectors, Linear Algebra and Geometry.
This collection of
exercises is designed to provide a framework for discussion in a junior level
linear algebra class conducted fairly regularly at Portland State University.
Topics covered includes: Matrices And Linear Equations, Vector Spaces , Linear
Maps Between Vector Spaces , Spectral Theory Of Vector Spaces, The Geometry Of
Inner Product Spaces , Adjoint Operators, Spectral Theory Of Inner Product
Spaces.
These notes are
intended for someone who has already grappled with the problem of constructing
proofs.This book covers the following topics: Gauss-Jordan elimination,
matrix arithmetic, determinants , linear algebra, linear transformations, linear
geometry, eigenvalues and eigenvectors.
This
book covers the following topics:
Ring Theory Background, Primary Decomposition and Associated
Primes, Integral Extensions, Valuation Rings, Completion, Dimension Theory,
Depth, Homological Methods and Regular Local Rings.
Author(s): Robert
B. Ash, Professor Emeritus, Mathematics