Tony Shaska

Tony Shaska

Associate Professor
Department of Mathematics and Statistics
Oakland University
146 Library Drive
Rochester, MI. 48309

Office: 546 Mathematics Science Center
E-mail: shaska[at]oakland.edu


MTH 2775: Linear Algebra

Description

Study of general vector spaces, linear systems of equations, linear transformations and compositions, Eigenvalues, eigenvectors, diagonalization, modeling and orthogonality. Provides a transition to formal mathematics.

Textbook

  • Lecture Notes in Linear Algebra, T. Shaska (will be provided in class for free)
  • Linear algebra with applications, Otto Bretscher
  • Course policies

    For all the problems and concerns you might have you must talk to me. No makeups will be given other then in case of documented emergencies. The use of cellular phones or any other electronic equipment is NOT allowed during lectures. No calculators of any kind are allowed. Further, I do not tolerate any kind of academic dishonesty. Appropriate measures according to Oakland University regulations will be taken for any case of cheating or breaking other rules. Attendance is mandatory!

    Detailed Syllabus

    A copy of the current semester of the detailed syllabus can be found here.

    Contents

    The following list of topics will be followed very closely.
  • Lecture 1: A word on analytic geometry
  • Lecture 2: Vectors in Physics and geometry
  • Lecture 3: Euclidean spaces and linear systems
  • Lecture 4: Row operations, algebra of matrices
  • Lecture 5: Introduction to vector spaces, bases and dimension
  • Lecture 6: Subspaces associated to a matrix, nullity and rank
  • Lecture 7: Sums, direct sums, direct products
  • Lecture 8: Midterm I
  • Lecture 9: Linear maps
  • Lecture 10: Matrices associated to linear maps, change of basis
  • Lecture 11: Linear transformations in geometry
  • Lecture 12: Determinants, characteristic polynomial
  • Lecture 13: Eigenvalues, Eigenvectors, eigenspaces
  • Lecture 14: Complex eigenvalues
  • Lecture 15: Diagonalizing matrices
  • Lecture 16: Midterm II
  • Lecture 17: Inner products, orthogonal bases
  • Lecture 18: Orthogonal transformations and orthogonal matrices
  • Lecture 19: Least squares
  • Lecture 20: Sylvestre’s theorem
  • Lecture 21: Quadratic and binary forms
  • Lecture 22: Midterm III
  • Lecture 23: Symmetric matrices
  • Lecture 24: Positive definite matrices
  • Lecture 25: Singular values and singular value decomposition
  • Lecture 26: Review