MAT2233

A comprehensive list of all undergraduate math courses at UTSA can be found here.

The Wikipedia summary of Linear Algebra and its history.

Topics List

Date	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
Week 1/2	1.1, 1.2, and 1.3	Systems of Linear Equations	Adding and subtracting equations Solving an equation for a specifed variable Equation for a line	Vectors and Matrices Gauss-Jordan elimination Rank of a matrix Matrix addition The product Ax Inner product Linear Combinations
Week 3/4	2.1, 2.2, 2.3, and 2.4	Linear Transformations	Basics of functions Inverse functions and the identity function Vectors and the Inner product	Linear transformations and their properties Geometry of Linear Transformations (rotations, scalings and projections) Matrix Products The Inverses of a linear transform
Week 5/6	3.1, 3.2, and 3.3	Bases and Linear Independence	Linear Combinations Dimension in Rn Image and kernel of a function	Image and Kernel of a linear transformation Span of a vector set Subspace of Rn Linear independence and basis Dimension Rank-nullity Theorem
Week 7/8	3.4	Similar Matrices and Coordinates	Conics (ellipses in particular) Equivalence Relations	Coordinates in a subspace of Rn Similar matrices Diagonal matrices
Week 9/10	5.1, 5.2, 5.3, and 5.4	Orthogonality	Parallel and perpendicular lines Absolute value function Basic trigonometric function Properties of inner products	Perpendicular vectors Magnitude of vectors Transpose of a Matrix Orthonormal vectors Orthogonal Projection Orthonormal Bases Gram-Schmidt process The Least Squares solution
Week 11/12	6.1, 6.2, and 6.3	Determinants	Summation notation Sgn function	Properties of Determinants Row operations and determinants Invertibility based on determinant Geometric Interpretation of the Determinant Cramer's rule
Week 13/14	7.1, 7.2, 7.3, and 8.1	Eigenvalues and Eigenvectors	Finding real roots of a polynomial Finding the kernel of a function	Diagonalization Finding eigenvalues Finding eigenvectors Geometric and algebraic multiplicity Spectral Theorem