Fundamentals of Matrix Algebra by Gregory Hartman
Fundamentals of Matrix Algebra - Table of Contents
- 1. Systems of Linear Equations
- 1.1 Introduction to Linear Equations
- 1.2 Using Matrices To Solve Systems of Linear Equations
- 1.3 Elementary Row Operations and Gaussian Elimination
- 1.4 Existence and Uniqueness of Solutions
- 1.5 Applications of Linear Systems
- 2. Matrix Arithmetic
- 2.1 Matrix Addition and Scalar Multiplication
- 2.2 Matrix Multiplication
- 2.3 Visualizing Matrix Arithmetic in 2D
- 2.4 Vector Solutions to Linear Systems
- 2.5 Solving Matrix Equations AX = B
- 2.6 The Matrix Inverse
- 2.7 Properties of the Matrix Inverse
- 3. Operations on Matrices
- 3.1 The Matrix Transpose
- 3.2 The Matrix Trace
- 3.3 The Determinant
- 3.4 Properties of the Determinant
- 3.5 Cramer’s Rule
- 4. Eigenvalues and Eigenvectors
- 4.1 Eigenvalues and Eigenvectors
- 4.2 Properties of Eigenvalues and Eigenvectors
- 5. Graphical Explorations of Vectors
- 5.1 Transformations of the Cartesian Plane
- 5.2 Properties of Linear Transformations
- 5.3 Visualizing Vectors: Vectors in Three Dimensions
What You Will Learn in Fundamentals of Matrix Algebra
Fundamentals of Matrix Algebra by Gregory Hartman is an open educational resource designed to introduce lower-division students to basic matrix theory. Accessing this fundamentals of matrix algebra gregory hartman pdf provides clear explanations of Gaussian elimination, matrix multiplication, and inverses.
The text systematically explores linear systems, vector spaces, linear independence, determinants, eigenvalues, and eigenvectors. Utilizing this gregory hartman matrix algebra pdf helps readers build procedural accuracy alongside conceptual understanding.
Designed as an entry-level fundamentals of matrix algebra book, this volume includes structured examples, visual diagrams, and practice exercises tailored for science, engineering, and mathematics students.
Book Details & Specifications
Title:
Fundamentals of Matrix Algebra by Gregory Hartman
Publisher:
Virginia Military Institute
Year:
2011
Pages:
248
Type:
PDF
Language:
English
ISBN-10 #:
1467901598
ISBN-13 #:
978-1467901598
License:
CC BY-NC 3.0 US
Amazon:
Amazon
About the Author: Gregory Hartman
The author Gregory Hartman
is a Professor of Mathematics at Virginia Military Institute (VMI).
He is the lead author of the APEX Calculus project and a strong advocate for open-access educational resources, specializing in developing clear, student-friendly mathematics textbooks.
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