Linear Algebra

The course is aimed at science and engineering students, especially applications in Artificial Intelligence and Data Science.

Catalog Description:
Study of general vector spaces, linear systems of equations, linear transformations and compositions, Eigenvalues, eigenvectors, diagonalization, modeling and orthogonality.

Contents

A word on Analytic Geometry, Vectors in Physics and Geometry % 1.1-1.5
Euclidean spaces, norm and dot product % 2.1-2.2
Matrices and their algebra, Gauss-Jordan elimination %2.3-2.6
Vector spaces, bases and dimension % 3.1-3.2
Subspaces, nullity and rank, sums, direct sums, direct products %3.3-3.4
Linear maps, isomorphisms %4.1-4.2
Matrices associated to linear maps, %4.3
Change of basis % 4.5
Linear transformations in geometry %4.6

Midterm I

Determinants, characteristic polynomial, Eigenvalues, Eigenvectors, eigenspaces % 5.1-5.2
Similar matrices, diagonalizing matrices
Inner products
Orthogonal bases, Gram-Schmidt orthogonalization
QR-factorization
Orthogonal transformations and orthogonal matrices
Sylvestre's theorem and dual space
Curve fitting
Quadratic forms
Symmetric matrices and spectral theorem

Midterm II

Graphing quadratic surfaces, principal axes theorem
Positive definite matrices
Singular Value Decomposition
Further topics
Review

Final Exam

Syllabus

Here is a detailed Syllabus

Books:

Linear Algebra, T. Shaska, Click here to get the free pdf file
Linear Algebra with Python, Springer

Project

Here is the description of the project