Overview
This textbook introduces the theory and application of linear systems, matrices, vector spaces, transformations, eigenvalues, and eigenvectors. Students learn both computational techniques and the underlying structure of linear mathematical systems that power modern scientific and technological applications.
Table of Contents
- Chapter 1: Systems of Linear Equations
- Chapter 2: Matrices and Matrix Operations
- Chapter 3: Determinants
- Chapter 4: Vector Geometry
- Chapter 5: Vector Spaces
- Chapter 6: Linear Transformations
- Chapter 7: Matrix Representations
- Chapter 8: Coordinate Systems and Change of Basis
- Chapter 9: Span, Independence, and Basis
- Chapter 10: Rank and Null Space
- Chapter 11: Orthogonality and Projections
- Chapter 12: Eigenvalues and Eigenvectors
- Chapter 13: Diagonalization
- Chapter 14: Applications of Linear Algebra
- Back Matter
Learning Outcomes
- Solve systems of linear equations using algebraic and matrix methods.
- Perform matrix operations and analyze matrix properties.
- Compute determinants and matrix inverses.
- Work with vectors in geometric and abstract settings.
- Understand vector spaces, subspaces, span, basis, and dimension.
- Analyze linear transformations and their matrix representations.
- Compute rank, nullity, eigenvalues, and eigenvectors.
- Apply orthogonality, projections, and diagonalization techniques.
- Use linear algebra to model problems in science, engineering, economics, and computing.