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| Systems Of Linear Equations | |
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| Introduction to Systems of Linear Equations | |
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| Gaussian Elimination and Gauss-Jordan Elimination | |
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| Applications of Systems of Linear Equations | |
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| Matrices | |
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| Operations with Matrices | |
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| Properties of Matrix Operations | |
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| The Inverse of a Matrix | |
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| Elementary Matrices | |
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| Applications of Matrix Operations | |
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| Determinants | |
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| The Determinant of a Matrix | |
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| Evaluation of a Determinant Using Elementary Operations | |
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| Properties of Determinants | |
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| Introduction to Eigenvalues | |
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| Applications of Determinants | |
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| Vector Spaces | |
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| Vectors in R" | |
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| Vector Spaces | |
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| Subspaces of Vector Spaces | |
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| Spanning Sets and Linear Independence | |
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| Basis and Dimension | |
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| Rank of a Matrix and Systems of Linear Equations | |
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| Coordinates and Change of Basis | |
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| Applications of Vector Spaces | |
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| Inner Product Spaces | |
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| Length and Dot Product in R" | |
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| Inner Product Spaces | |
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| Orthonormal Bases: Gram-Schmidt Process | |
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| Mathematical Models and Least Squares Analysis | |
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| Applications of Inner Product Spaces | |
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| Linear Transformations | |
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| Introduction to Linear Transformations | |
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| The Kernel and Range of a Matrices for Linear Transformations | |
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| Transition Matrices and Similarity | |
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| Applications of Linear Transformations | |
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| Eigenvalues and Eigenvectors | |
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| Eigenvalues and Eigenvectors | |
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| Diagonalization | |
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| Symmetric Matrices and Orthogonal Diagonalization | |
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| Applications of Eigenvalues and Eigenvectors | |
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| Complex Vector Spaces (Online) | |
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| Complex Numbers | |
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| Conjugates and Division of Complex Numbers | |
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| Polar Form and DeMoivre's Theorem | |
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| Complex Vector Spaces and Inner Products | |
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| Unitary and Hermitian Matricies | |