Vectors and spaces. Vectors : Vectors and spaces Linear combinations and spans : Vectors and spaces Linear dependence and independence : Vectors and spaces. Subspaces and the basis for a subspace : Vectors and spaces Vector dot and cross products : Vectors and spaces Matrices for solving systems by elimination : Vectors and spaces Null space and column space : Vectors and spaces.
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Matrix transformations. Functions and linear transformations : Matrix transformations Linear transformation examples : Matrix transformations Transformations and matrix multiplication : Matrix transformations. Inverse functions and transformations : Matrix transformations Finding inverses and determinants : Matrix transformations More determinant depth : Matrix transformations Transpose of a matrix : Matrix transformations. Alternate coordinate systems bases.
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Orthogonal complements : Alternate coordinate systems bases Orthogonal projections : Alternate coordinate systems bases Change of basis : Alternate coordinate systems bases. Orthonormal bases and the Gram-Schmidt process : Alternate coordinate systems bases Eigen-everything : Alternate coordinate systems bases.
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