Math 251: Matrix Algebra for Engineers

Videos

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)