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Mastering Linear Algebra: An Introduction with Applications

Linear Algebra: Powerful Transformations
Vectors: Describing Space and Motion
Linear Geometry: Dots and Crosses
Matrix Operations
Linear Transformations
Systems of Linear Equations
Reduced Row Echelon Form
Span and Linear Dependence
Subspaces: Special Subsets to Look For
Bases: Basic Building Blocks
Invertible Matrices: Undoing What You Did
The Invertible Matrix Theorem
Determinants: Numbers That Say a Lot
Eigenstuff: Revealing Hidden Structure
Eigenvectors and Eigenvalues: Geometry
Diagonalizability
Population Dynamics: Foxes and Rabbits
Differential Equations: New Applications
Orthogonality: Squaring Things Up
Markov Chains: Hopping Around
Multivariable Calculus: Derivative Matrix
Multilinear Regression: Least Squares
Singular Value Decomposition: So Cool
General Vector Spaces: More to Explore