Math 205: Linear Algebra
Math 205: Linear Algebra
Introductory Linear Algebra with Applications
Introductory Linear Algebra with Applications
Module 1 Linear systems:
lecturenotes: Linear systems
videos: linear equations, elimination, solving linear systems, Gauss elimination, Gauss Jordan elimination, echelon and row reduced echelon form, flavors of solutions, overview
Module 2 Matrices and determinants:
lecturenotes: Matrices and determinants
videos: introduction to matrices, matrix addition, matrix multiplication, elementary matrices, outline, elementary matrices revisit, determinants, properties of determinants, Cramer's rule, inverses using determinants, inverses using Gauss-Jordan elimination,
Module 3 Vector spaces and subspaces
lecturenotes: Vector spaces and subspaces
videos: motivation, definition, examples, elementary theorem, subspaces, linear combination and span, null space and column space
Module 4: Linear independence, span and bases
lecturenotes:
videos: linear independence, related theorems, geometric representations, theorem 5.3.3 , basis, dimension, plus/minus theorem, theorem 5.4.5, more theorems, null space and column space.
Module 5: Linear transformations
lecturenotes: linear transformations
videos: linear maps, linear maps and basis, rotation matrix,
Module 6: Orthogonality and Gram-Schmidt process
lecturenotes: Orthogonality and Gram-Schmidt process
videos: innerproduct, norm, orthogonal decomposition, Gram-Schmidt process
Module 7: Eigenvalues and Eigenvectors
lecturenotes: Eigenvalues and Eigenvectors
videos: introduction, computation, similarity and diagonalization, applications
Module 8: Applications
lecturenotes:
videos: