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Welcome to the course website for Linear Algebra and Applications . This course is an introduction to the subject of linear algebra which arises in many branches of mathematics and in applications. This class aims to cover both core theoretical topics in linear algebra as well as practical aspects for how to analyze and solve linear systems. More information can be found in the syllabus below and on the course website. I look forward to working with you this quarter.
Please note this course will be primarily administered through the Gauchospace website. Please log-in there for additional and update-to-date information and resources.
Selection of Topics
- Introduction to Linear Algebra and Motivations
- Systems of Linear Equations
- Row Reduction and Echelon Forms
- Vector Equations
- The Matrix Equation Ax = b
- Solution Sets of Linear Systems
- Applications of Linear Systems
- Linear Independence
- Introduction to Linear Transformations
- The Matrix of a Linear Transformation
- Applications in Business, Science, and Engineering
- Matrix Algebra
- Motivations and Applications
- Matrix Operation
- The Inverse of a Matrix
- Characterizations of Invertible Matrices
- Applications to Computer Graphics
- Subspaces of Rn
- Dimension and Rank
- Determinants
- Motivations and Applications
- Introduction to Determinants
- Properties of Determinants
- Cramer’s Rule, Volume, and Linear Transformations
- Vector Spaces
- Motivations and Applications
- Vector Spaces and Subspaces
- Null Spaces, Column Spaces, and Linear Transformations
- Linearly Independent Sets; Bases
- Coordinate Systems
- The Dimension of a Vector Space
- Rank
- Change of Basis
- Applications to Difference Equations
- Applications to Markov Chains
- Eigenvalues and Eigenvectors
- Motivations and Applications
- Eigenvectors and Eigenvalues
- The Characteristic Equation
- Discrete Dynamical Systems
- Orthogonality and Least Squares
- Motivations and Applications
- Inner Product, Length, and Orthogonality
- Orthogonal Sets
- Orthogonal Projections
- Least-Squares Problems
Please see the Gauchospace website for this course for more information and materials: