Elementary Linear Algebra

Covers the basic problems of linear algebra: solving linear equations, constructing a basis for a vector space, constructing a matrix which represents a linear transformation, eigenvalue-eigenvector and diagonalization.

**Tag(s):**
Linear Algebra

**Publication date**: 31 Dec 2001

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
n/a

**Views**: 24,752

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 25 Jun 2007 09:41:08

Elementary Linear Algebra

Covers the basic problems of linear algebra: solving linear equations, constructing a basis for a vector space, constructing a matrix which represents a linear transformation, eigenvalue-eigenvector and diagonalization.

Excerpts from the Preface:

Linear algebra, as we know it today, furnishes a beautiful mathematical structure; the integral parts of the structure are powerful tools for engineers, scientists, and mathematicians. Students in these diverse fields come to linear algebra with a common background: They have learned mathematics by working problems and studying examples. With this idea in mind, I have drawn the reader's attention in this text to what I consider to be the five basic problems of linear algebra:

1. The problem of solving linear equations

2. The problem of constructing a basis for a vector space

3. The problem of constructing a matrix which represents a linear transformation

4. The eigenvalue-eigenvector problem

5. The diagonalization problem

These problems give the students landmarks to look for and skills to master in the course.

Of course, the solutions of the five basic problems result in the important theorems of linear algebra. These are stated accurately and then proved unless the proof lies beyond the scope of elementary linear algebra. My hope is that the reader will come to see the structure of linear algebra as supported by the five main beams of the five basic problems with the detail fleshed out by examples, applications, and theorems.

I have given a wide variety of applications of linear algebra. The lion's share are slanted toward science and engineering, however. Presenting applications can be tricky in that enough flavor of the origin of the application must be given to convince the student that the example is not bogus, yet not too much detail of the application must appear to scare away a novice. For example, the presentation of some linear equations arising in structures is the important point, not a minicourse in statics and dynamics. I believe that the applications have been given in appropriate detail and that the students will be able to see and handle the linear algebraic aspects of the applied examples once they are laid out.

Intended Audience:

Except for those sections with the word calculus in the section title, the reader need only be equipped with knowledge of the derivative and integral in an elementary fashion. I have put the deeper connections of calculus and linear algebra in these separate sections so that the interested reader can find them easily.

Linear algebra, as we know it today, furnishes a beautiful mathematical structure; the integral parts of the structure are powerful tools for engineers, scientists, and mathematicians. Students in these diverse fields come to linear algebra with a common background: They have learned mathematics by working problems and studying examples. With this idea in mind, I have drawn the reader's attention in this text to what I consider to be the five basic problems of linear algebra:

1. The problem of solving linear equations

2. The problem of constructing a basis for a vector space

3. The problem of constructing a matrix which represents a linear transformation

4. The eigenvalue-eigenvector problem

5. The diagonalization problem

These problems give the students landmarks to look for and skills to master in the course.

Of course, the solutions of the five basic problems result in the important theorems of linear algebra. These are stated accurately and then proved unless the proof lies beyond the scope of elementary linear algebra. My hope is that the reader will come to see the structure of linear algebra as supported by the five main beams of the five basic problems with the detail fleshed out by examples, applications, and theorems.

I have given a wide variety of applications of linear algebra. The lion's share are slanted toward science and engineering, however. Presenting applications can be tricky in that enough flavor of the origin of the application must be given to convince the student that the example is not bogus, yet not too much detail of the application must appear to scare away a novice. For example, the presentation of some linear equations arising in structures is the important point, not a minicourse in statics and dynamics. I believe that the applications have been given in appropriate detail and that the students will be able to see and handle the linear algebraic aspects of the applied examples once they are laid out.

Intended Audience:

Except for those sections with the word calculus in the section title, the reader need only be equipped with knowledge of the derivative and integral in an elementary fashion. I have put the deeper connections of calculus and linear algebra in these separate sections so that the interested reader can find them easily.

Tweet

About The Author(s)

No information is available for this author.

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
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors