MAT2233

From Department of Mathematics at UTSA
Revision as of 07:43, 7 July 2020 by James.kercheville (talk | contribs) (Made edits to first 6 topics in the table)
Jump to navigation Jump to search

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

  • Vectors and Matrices
  • Gauss-Jordan elimination
Week 2
1.3

Solutions of Linear Systems

  • Rank of a matrix
  • Matrix addition
  • The product Ax
  • Inner product
  • Linear Combinations


Week 3
2.1 and 2.2


Linear Transformations

  • Linear transformations and their properties
  • Geometry of Linear Transformations (rotations, scalings and projections)
Week 4
2.3 and 2.4


Matrix Products and Inverses

  • 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

  • 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

  • Subspaces in Different Dimensions
  • Bases and Linear independence
  • Characterizations of Linear Independence


Week 5
3.3

[[The Dimension of Subspaces in Rn]]

  • Dimension of the Image
  • Rank-nullity theorem
  • Various bases in Rn


Week 7/8
3.4


Similar Matrices and Coordinates

  • 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