As an instructor, I prepared these PDFs as class notes for Applied Linear Algebra. The class covered chapters in Peter Olver’s “Applied Linear Algebra” It includes example problems which have been worked out in some detail. I hope you find these useful.
1p1_1p3_Linear_Systems_Matrices_Vectors_Gaussian_Elimination
1p4_1p5_Pivoting_Permutations_Inverse_Matrices/a>
1p6_Transposes_and_Symmetric_Matrices
1p8_General_Linear_Systems
1p9_Determinants
2p1_Real_Vector_Spaces
2p2_Subspaces
2p3_Span_and_Linear_Independence
2p4_Basis_and_Dimension
2p5_Fundamental_Matrix_Subspaces
2p6_Graphs_and_Digraphs
3p1_Inner_Products
3p2_Cauchy_Schwarz_and_Triangle_Inequalities
3p3_Norms
3p4_Positive_Definite_Matrices
3p5_Completing_the_square
4p1_Orthogonal_and_Orthonormal_Bases
4p2_Gram_Schmidt_Process
4p3_Orthogonal_Matrices
4p4_Orthogonal_Projections_and_Subspaces_fredholm_alternative
5p2_Minimization_of_Quadratic_Functions
8p2_Eigenvalues_and_Eigenvectors