This note covers
the following topics: Motivation, linear spaces, and isomorphisms, Subspaces,
linear dependence and independence, Bases, Dimension, direct sums, and
isomorphism, Quotient spaces and dual spaces, Linear maps, nullspace and range,
Nullity and rank, Matrices, Changing bases, Conjugacy, types of operators, dual
space, determinants.
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.
This book is
addressed primarely to second and third year college engineering students who
have already had a course in calculus and analytic geometry. It is the result of
lecture notes given by the author at Arkansas Tech University. Topics covered
includes: Linear Systems of Equations, Matrices, Determinants, The Theory of
Vector Spaces, Eigenvalues and Eigenvectors, Linear Transformation.
This note explains
the following topics: Vector spaces, The field of complex numbers, Linear maps,
Subspaces, Matrices, Linear independence and dimension, Ranks, Linear maps and
matrices, Determinants, Eigenvalues and Eigenvectors.
This
note emphasize the concepts of vector spaces and linear transformations as
mathematical structures that can be used to model the world around us. Topics
covered includes: Gaussian Elimination, Elementary Row Operations, Vector
Spaces, Linear Transformations, Matrices, Elementary Matrices and Determinants,
Eigenvalues and Eigenvectors, Diagonalization, Kernel, Range, Nullity, Rank,
Gram-Schmidt and Orthogonal Complements.
These notes are concerned with algebraic number theory, and the sequel
with class field theory. Topics covered includes: Preliminaries from Commutative
Algebra, Rings of Integers, Dedekind Domains- Factorization, The Unit Theorem,
Cyclotomic Extensions- Fermat’s Last Theorem, Absolute Values- Local Fieldsand
Global Fields.
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