Linear Algebra And Analysis

This is on linear algebra and its interaction with analysis. It emphasizes the main ideas, both algebraic and geometric and attempts to present these ideas as quickly as possible without being overly terse.

**Tag(s):**
Linear Algebra

**Publication date**: 13 Jan 2018

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
619 pages

**Views**: 4,426

Linear Algebra And Analysis

This is on linear algebra and its interaction with analysis. It emphasizes the main ideas, both algebraic and geometric and attempts to present these ideas as quickly as possible without being overly terse.

From the Preface:

Kuttler wrote:This is on linear algebra and its interaction with analysis. It emphasizes the main ideas, both algebraic and geometric and attempts to present these ideas as quickly as possible without being overly terse. The emphasis will be on arbitrary fields in the first part and then later geometric ideas will be included in the context of the usual fields of R and C. The first part is on linear algebra as a part of modern algebra. It avoids cluttering the presentation with geometric and analytic ideas which are really not essential to understanding these theorems. The second part is on the role of analysis in linear algebra. It is like baby functional analysis. Some analysis ideas do in fact creep in to the first part, but they are generally fairly rudimentary, occur as examples, and will have been seen in calculus. It may be that increased understanding is obtained by this kind of presentation in which that which is purely algebraic is presented first. This also involves emphasizing the minimum polynomial more than the characteristic polynomial and postponing the determinant. In each part, I have included a few related topics which are similar to ideas found in linear algebra or which have linear algebra as a fundamental part.The third part of the book involves significant ideas from analysis which depend on linear algebra.

The book is a re written version of an earlier book. It also includes several topics not in this other book including a chapter which is an introduction to modules and rings and much more material on analysis. However, I am not including topics from functional analysis so much. Instead, I am limiting the topics to the standard analysis involving derivatives and integrals. In fact, if everything which uses linear algebra were presented, the book would be much longer. It is limited to topics that I especially like and emphasizes finite dimensional situations.

Tweet

About The Author(s)

Kenneth Kuttler is Professor in the Department of Mathematics at Brigham Young University. His primary area of research is Partial Differential Equations and Inclusions. He works on abstract methods for determining whether problems of this sort are well posed. Lately, he has been working on the mathematical theory of problems from contact mechanics including friction, wear, and damage. He has also been studying extensions to stochastic equations and inclusions.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Rexx
Microsoft .NET
Perl
PHP
R
Python
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors