Introduces and provides models for application of the concepts of vector algebra. Topics include finite dimensional vector spaces and their geometric significance; representing and solving systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion; matrices; determinants; linear transformations; quadratic forms; eigenvalues and eigenvectors; and applications in science and engineering.
Linear Algebra and Its Applications 5th Edition (Lay) - Chapters 1-7
Textbook Link| Full Linear Algebra Notes |
| Chapter 1 - Linear Equations in Linear Algebra (1/21/25 - 2/11/25) |
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 Linear Models in Business, Science, and Engineering |
Notes |
| Chapter 2 - Matrix Algebra (2/12/25 - 2/22/25) |
Matrix Operations The Inverse of a Matrix Characterizations of Invertible Matrices Matrix Factorizations |
Notes |
| Chapter 3 - Determinants (2/24/25 - 3/1/25) |
Introduction to Determinants Properties of Determinants Cramer's Rule, Volume, and Linear Transformations |
Notes |
| Chapter 4 - Vector Spaces (3/3/25 - 3/20/25) |
Vector Spaces and Subspaces Null Spaces, Column Spaces, Row Spaces, and Linear Transformations Linearly Independent Sets; Bases Coordinate Systems The Dimension of a Vector Space Change of Basis |
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| Chapter 5 - Eigenvalues and Eigenvectors (3/24/25 - 4/3/25) |
Eigenvectors and Eigenvalues The Characteristic Equation Diagonalization Applications of Differential Equations |
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| Chapter 6 - Orthogonality and Least Squares (4/4/25 - 4/22/25) |
Inner Product, Length, and Orthogonality Orthogonal Sets Orthogonal Projections The Gram-Schmidt Process Least-Squares Problems Machine Learning and Linear Models Inner Product Spaces |
Notes |
| Chapter 7 - Symmetric Matrices and Quadratic Forms (4/28/25 - 5/1/25) |
Diagonalization of Symmetric Matrices Quadratic Forms |
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