Course Notes for Math 251
Course Notes for Math 251
Textbook
David Poole, Linear Algebra, 4th edition
Section 1.1 The Geometry and Algebra of Vectors
Video: Intro to Vectors (2 minutes)
Video: Intro to Linear Combinations (4 minutes)
Section 1.2 Length and Angle: The Dot Product
Video: The Vector Cross Product (7 minutes)
Picture: Right hand rule
Section 1.3 Lines and Planes
Video: General and Normal Form (3 minutes)
Video: Vector and Parametric Form (6 minutes)
Video: Distance between a point and a line (9 minutes)
Video: Equation of a plane through three points (6 minutes)
Section 2.1 Introduction to Systems of Linear Equations
Section 2.2 Direct Methods for Solving Linear Systems
Handout: Row Echelon Form (by George Ballinger)
Video: Gaussian Elimination (12 minutes)
Video: Gauss-Jordan Elimination (13 minutes)
Section 2.3 Spanning Sets and Linear Independence
Video: Span (7 minutes)
Video: Linear Independence (10 minutes)
Handout: Solution of a linear system
Section 2.4 Applications
Planar Trusses (for Civil Engineering students)
Section 3.1 Matrix Operations
Video: Matrix Operations (9 minutes)
Section 3.2 Matrix Algebra
Handout: Properties of Matrices
Video: Span of a set of matrices (12 minutes)
Section 3.3 The Inverse of a Matrix
Video: The Inverse of a Matrix (8 minutes)
Video: Elementary Matrices (10 minutes)
Section 3.4 LU Factorization
Video: LU Factorization (8 minutes)
Video: Solving using LU (6 minutes)
Section 3.5 Subspaces, Basis, Dimension, and Rank
Video: Subspaces (9 minutes)
Video: Row Space, Column Space, and Null Space (8 minutes)
Section 3.6 Introduction to Linear Transformations
Video: Standard Matrix of a Linear Transformation (8 minutes)
Video: Image under a Linear Transformation (7 minutes)
Section 4.1 Introduction to Eigenvalues and Eigenvectors
Video: Eigenvalues and Eigenvectors (9 minutes)
Video: Finding Eigenvalues and Eigenvectors (17 minutes)
Section 4.2 Determinants
Video: Cramer's Rule (7 minutes)
Video: The adjoint formula to find the inverse (7 minutes)
Section 4.3 Eigenvalues and Eigenvectors of n x n Matrices
Handout: Fundamental theorem of invertible matrices
Handout: Review of eigenvalues and eigenvectors
Section 4.4 Diagonalization
Systems of DEs (not tested in Math 251 but useful in Math 252 next semester)
Video: Diagonalization (7 minutes)
Video: Powers of a Matrix and Diagonalization (8 minutes)
Section 5.1 Orthogonality in R^n
Video: Calculations with an Orthogonal Basis (3 minutes)
Video: Orthogonal Matrices (4 minutes)
Section 5.2 Orthogonal Complements and Projections
Video: Orthogonal Complements (7 minutes)
Video: Orthogonal Decompositions (8 minutes)
Section 5.3 Gram-Schmidt Process and QR Factorization
Video: The Gram-Schmidt Process (7 minutes)
Video: QR Factorization (9 minutes)
Section 5.4 Orthogonal Diagonalization of Symmetric Matrices
Video: Orthogonal Diagonalization (11 minutes)
Section 7.3 Least Squares Approximation
Video: Least Squares Approximation (8 minutes)