MATH-3660 lecture slides

A partial list of lecture slides can be found here. This list is not complete (and that is intentional). Lectures that are designed to be more interactive will not have corresponding slides. Also, please be aware that the slides do not reflect the deeper discussion involved in each class meeting.

• Lecture 1: Vectors
• Lecture 2: Linear dependence/independence
• Lecture 3: Span and subspaces
• Lecture 4: Basis and dimension of subspaces
• Lecture 5: Inner product spaces
• Lecture 6: Things that can be considered as “vectors”
• Lecture 7: Linear/affine functions and regression models
• Lecture 8: Matrices as representations of linear functions
• Lecture 9: Matrix-matrix products
• Lecture 10: Rank and inverse of matrices
• Lecture 11: Different types of matrices
• Lecture 12: Matrices from applications
• Lecture 13: Orthogonal group and special orthogonal group (optional)
• Lecture 14: Systems of linear equations
• Lecture 15: Least squares problem
• Lecture 16: QR decomposition
• Lecture 17: Eigenvalues and eigenvectors
• Lecture 18: Eigenvalue decomposition
• Lecture 19: Singular values
• Lecture 20: Singular value decomposition (optional)

We also have additional lectures discussions on specific aspects applications of things we learned.

• Application 1: Images and pixels
• Application 2: Sound signal
• Application 3: Covariance matrices