Topics in Linear Algebra

Department: 
MATH
Course Number: 
4305
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every semester

Linear algebra in R^n, standard Euclidean inner product in R^n, general linear spaces, general inner product spaces, least squares, determinants, eigenvalues and eigenvectors, symmetric matrices

Prerequisites: 

MATH 1502 OR MATH 1512 OR MATH 1555 OR MATH 1504 ((MATH 1552 OR MATH 15X2 OR MATH 1X52) AND (MATH 1522 OR MATH 1553 OR MATH 1554 OR MATH 1564 OR MATH 1X53))

Course Text: 

At the level of Linear Algebra with Applications, Bretscher

Topic Outline: 
  • Linear systems. Gauss-Jordan elimination (row reduction)
  • Linear transformations in R^n and their matrices
  • Composed transformations and matrix products. The inverse
  • Subspaces, bases, dimension, coordinates with respect to bases
  • Image and kernel. Rank and nullity
  • General linear spaces and subspaces
  • Linear transformations in general linear spaces. Matrices with respect to bases
  • Orthogonal projections
  • Orthonormal bases, Gram-Schmidt process, and QR factorization
  • Least squares
  • General Inner product spaces
  • Determinants. Geometric properties
  • Eigenvalues and eigenvectors
  • Diagonalization. Matrix iterations
  • Orthogonal diagonalization of symmetric matrices and quadratic forms
  • Singular value decomposition