Videos for Matrix Algebra for Engineers (Camosun Math 251) These videos will help you review some of the basic concepts in the course. The length of each video appears in brackets beside the title. Watching the videos is not a replacement for attending class or studying your class notes. 1.1 Intro to Vectors (2 mins) 1.1 Intro to Linear Combinations (4 mins) 1.2 A Proof about The Dot Product (5 mins) 1.2 Scaling Vectors (4 mins) 1.3 General and Normal Form (3 mins) 1.3 Vector and Parametric Form (6 mins) 1.3 Distance Between a Point and a Line (9 mins) Cross Product: Equation of a Plane Through Three Points (6 mins) Cross Product: Area of a Triangle in 3-d (4 mins) Determinants: Area of a Parallelogram in 2-d (3 mins) Determinants: Volume of a Parallelepiped in 3-d (9 mins) 2.2 Gaussian Elimination (12 mins) 2.2 Gauss-Jordan Elimination (13 mins) 2.3 Span (7 mins) 2.3 Linear Independence (11 mins) 3.1 Matrix Operations (9 mins) 3.1 Powers of a Matrix (10 mins) 3.2 Span of a Set of Matrices (12 mins) 3.2 A Proof about the Transpose (3 mins) 3.3 The Inverse of a Matrix (8 mins) 3.3 Elementary Matrices (10 mins) 3.4 LU Factorization (8 mins) 3.4 Solving using LU (6 mins) 3.5 Subspaces (9 mins) 3.5 Rowspace, Columnspace and Nullspace (8 mins) 3.6 Standard Matrix of a Linear Transformation (8 mins) 3.6 Image Under a Linear Transformation (7 mins) 4.1 Eigenvalues and Eigenvectors (9 mins) 4.1 The Geometry of Eigenvectors (7 mins) 4.2 Cramer's Rule (7 mins) 4.2 The Adjoint Formula for an Inverse Matrix (7 mins) 4.3 Geometric Multiplicity (6 mins) 4.3 Algebraic Multiplicity (13 mins) 4.3 A Proof about Eigenvectors (5 mins) 4.4 Diagonalization (7 mins) 4.4 Powers of a Matrix and Diagonalization (8 mins) 5.1 Calculations with an Orthogonal Basis (3 mins) 5.1 Orthogonal Matrices (4 mins) 5.2 Orthogonal Complements (7 mins) 5.2 Orthogonal Decompositions (8 mins) 5.3 The Gram-Schmidt Process (7 mins) 5.3 QR Factorization (9 mins) 5.4 Orthogonal Diagonalization (11 mins) 5.4 The Spectral Decomposition (6 mins) 7.3 Least Squares Approximation (8 mins) Appendix C: The Algebra of Complex Numbers (3 mins) Appendix C: Complex Eigenvalues and Eigenvectors (12 mins)