Course overview (MAT 343: Applied Linear Algebra at Arizona State University)

1.1 Systems of Linear Equations and Matrices

1.2 Row Echelon Form and Parametric Solutions

1.3 Matrix Arithmetic and the Consistency Theorem

1.4 Matrix Algebra and Inverses

1.5 Elementary Matrices and the LU Decomposition

2.1 The Determinant of a Matrix

2.2 Properties of Determinants

3.1 Vector Spaces

3.2 Subspaces

3.3 Linear Independance

3.4 Basis and Dimension

3.5 Change of Basis

3.6 Row Space and Column Space

4.1 Linear Transformations

4.2 Matrix Representation of Linear Transformations

5.1 Scalar and Vector Projections

5.2 Orthogonal Subspaces

5.3 Least Squares Solutions

5.4 Inner Product Spaces and Induced Norms

5.5 Orthonormal Sets

5.6 The Gram-Schmidt Orthonormalization Procedure

6.1 Eigenvalues and Eigenvectors

6.3 Diagonalization

6.5 Singular Value Decomposition