COMS 3251

Topic 1
Introduction to vectors and matrices; linear combinations, lengths and dot products
Topic 2
Solving linear system of equations; elimination technique; rules for matrix operations, inverses, transposes and permutations
Topic 3
Vector spaces and subspaces; four fundamental subspaces; independence, basis span dimension
Topic 4
Orthogonality; projections, computing orthonormal basis and the Gram-Schmidt process
Topic 5
(optional)
Determinants and its properties; permutations and cofactors, Cramer's rule and volume
Topic 6
Eigenvectors and Eigenvalues; diagonalization of a matrix; positive definite matrices
Topic 7
Singular value decomposition (SVD) and its geometry
Topic 8
Linear Transformations and finding a good basis
Topic 9
(if time permits)
Applications in Engineering, Economics, Graphics, Cryptography, etc.

Software
MATLAB: download info, learning the basics.
Python: download info, tutorial
LaTeX: download info, learning the basics, typesetting common math formulas.
Expected Background
Calculus: Calc I, II and III (or equivalent)
Programming: COMS 1004 or COMS 1007 (or equivalent)

Homework submission & formatting
Homeworks will contain a mix of programming and written assignments.

Please include your name and UNI on the first page of the written assignment and at the top level comment of your programming assignment.

The written segment of the homework (including plots and comparative experimental studies) must be submitted via Gradescope, and (if the homeworks specifies) the a tarball of the programming files should be handed in by the specified due dates. No late homeworks will be accepted.
Collaboration
Discussion of the homework problems is encouraged, but you must write the solutions individually (or as specified in the homeworks). General discussion on problem clarification and possible approaches can be discussed with others over the course discussion board. Everyone must write up their own solutions independently.
Late submissions
No late homeworks will be accepted.
Academic rules of conduct
Students are expected to adhere to the Academic Honesty policy of the Computer Science Department, this policy can be found in full here.
Violations
Violation of any portion of these policies will result in a penalty to be assessed at the instructor's discretion. This may include receiving a zero grade for the assignment in question and a failing grade for the whole course, even for the first infraction.

Computational Linear Algebra