Fall 2017

Prof Yair Glasner

Course Content

  • Fields: definitions, the field of complex numbers.
  • Linear equations: elementary operations, row reduction, homogeneous and inhomogeneous systems, representations of the solutions.
  • Vector spaces: examples, subspaces, linear dependence, bases, dimension.
  • Matrix algebra: matrix addition and multiplication, elemetary operations, the inverse of a matrix, the determinant, Cramer’s rule.
  • Linear transformations: examples, kernel and image, matrix representation.
  • Diagonalization: eigenvectors and eigenvalues, the characteristic polynomial, applications.
  • Bilinear forms.
  • Finite dimensional inner product spaces.
  • Operators on finite dimensional inner product spaces: the adjoint, self adjoint operators, normal operators, diagonalization of normal operators.

Course Catalogue: 201.1.9641