Lecture notes
LecLecture 1: Introduction
Lecture 2: Linear Systems
Lecture 3: Some applications of linear systems
Lecture 4: Inverse of a matrix
Lecture 5: Conditions for invertibility
Lecture 6: Determinants
Lecture 7: Determinants (contd.), LU decomposition
Lecture 8: LU decomposition (contd.)
Lecture 9: Complexity of Gaussian elimination & LU decomp.
Lecture 10: Vector spaces and subspaces
Lecture 11: Null space of A, rank of A
Lecture 12: Basis and dimension
Lecture 13: Matrix of a lin. transformation
Lecture 14: Change of basis matrix
Lecture 15: Rotations, reflections, shears
Lecture 16: Computer graphics
Lecture 17:Kernel and Range of a lin. transformation
Lecture 18: Applications of rank-nullity-1
Lecture 19: Applications of rank-nullity-2
Lecture 20: Application of linear algebra to recurrence relations
Lecture 21: Inner Product Spaces
Lecture 22: Orthogonal sets and bases
Lecture 23: Orthogonal Projections
Lecture 24: Pattern recognition
Lecture 25: Gram-Schmidt process, QR factorization
Lecture 26: Least squares approximation
Lecture 27: Least squares (contd.)
Lecture 28: Eigenvalues, Eigenvectors
Lecture 29: Diagonalizability of square matrices
Lecture 30: Generalized Eigenvectors
Lecture 31: Jordan forms
Lecture 32-34: Jordan forms (contd.)
Lecture 35: Singular Value Decomposition
Lecture 36: Difference equations
Lecture 37: Brief intro to Markov chains, Google PageRank