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	1.1, 1.2	Systems of Linear Equations	Adding and multiplying equations by constants Solving Equations	Vectors and Matrices Gauss-Jordan elimination
Week 2	1.3	Solutions of Linear Systems	Gauss-Jordan elimination Equation for a line	Rank of a matrix Matrix addition The product Ax Inner product Linear Combinations
Week 3	2.1 and 2.2	Linear Transformations	Range of a Function Transformations of Functions	Linear transformations and their properties Geometry of Linear Transformations (rotations, scalings and projections)
Week 4	2.3 and 2.4	Matrix Products and Inverses	Linear Combinations Inverse Functions Vectors and the Inner product	Matrix Products (both inner product and row-by-column methods) The Inverses of a linear transform
Week 6	3.1	Image and Kernel of a Linear Transform	Solutions of Linear Systems Image of a Function Kernel of a Function	The image of a Linear transformation The kernel of a linear transformation Span of a set of vectors Alternative characterizations of Invertible matrices
Week 6	3.2	Bases and Linear Independence	Solutions of Linear Systems Image and Kernel of a Linear Transform	Subspaces in Different Dimensions Bases and Linear independence Characterizations of Linear Independence
Week 5	3.3	The Dimension of Subspaces	Image of a Function Bases and Linear Independence Linear transformations	Dimension of the Image Rank-nullity theorem Various bases in Rn
Week 7/8	3.4	Similar Matrices and Coordinates	Bases and Linear Independence Equivalence Relations	Coordinates in a subspace of Rn Similar matrices Diagonal matrices
Week 9	5.1, 5.2, 5.3, and 5.4	Orthogonality	Parallel and perpendicular lines Absolute value function Basic trigonometric function Properties of inner products	Transpose of a Matrix Cauchy-Schwarz Inequality Orthonormal vectors Orthogonal complement Orthogonal Projection Orthonormal Bases
Week 10	5.1, 5.2, 5.3, and 5.4	Gram-Schmidt Process	Unit vectors Inner products Orthonormal bases Subspaces of Rn	Gram-Schmidt process The Least Squares solution
Week 11	6.1, 6.2, and 6.3	Determinants	Summation notation Sgn function	Properties of Determinants Sarrus's Rule Row operations and determinants Invertibility based on determinant
Week 12	6.1, 6.2, and 6.3	Cramer's Rule	Properties of Determinants linear Systems Invertible matrices	Parrallelepipeds in Rn Geometric Interpretation of the Determinant Cramer's rule
Week 13	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
Week 14	7.1, 7.2, 7.3, and 8.1	Spectral Theorem	Transpose of a matrix Basis Orthogonal matrices Diagonal matrices	Symmetric matrices Spectral Theorem