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# 101 - LINEAR ALGEBRA This course will cover 1 Matrices...

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1 LINEAR ALGEBRA This course will cover: 1. Matrices, Vectors, and Systems of Linear Equations 1.1 Matrices and vectors 1.2 Linear combination, matrix-vector products, and special matrices 1.3 Systems of linear equations 1.4 Gaussain elimination 1.6 The span of a set of vectors 1.7 Linear dependence and linear independence 2. Matrices and Linear Transformations 2.1 Matrix multiplication 2.3 Invertibility and elementary matrices 2.4 The inverse of a matrix 2.5 Partitioned matrices and block multiplication 2.6 The LU decomposition of a matrix 2.7 Linear transformations and matrices 2.8 Composition and invertibility of linear transformations 3. Determinants 3.1 Cofactor expansion 3.2 Properties of determinants 4. Subspaces and Their Properties 4.1 Subspaces 4.2 Basis and dimension 4.3 The dimension of subspaces associated with a matrix 4.4 Coordinate systems 4.5 Matrix representations of linear operators 5. Eigenvalues, Eigenvectors, and Diagonalization 5.1 Eigenvalues and eigenvectors 5.2 The characteristic polynomial 5.3 Diagonalization of matrices 5.4 Diagonalization of linear operators 5.5 Jordan form

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