0366.1112.04 LINEAR ALGEBRA II

Lecturer:
Dany Leviatan
Spring Semester 2005.
Time and place:
Monday     10.00-12.00 in Melamed Hall
Thursdays 08.00-10.00 in Lev Hall

Grade: An examination at the end of the semester

The syllabus of the course

  1. POLYNOMIALS
    The ring of polynomials;
    Division with remainder, greatest common denominator;
    Primes and prime factorization;
    Roots of polynomials and the fundamental theorem of algebra.
  2. INVARIANT SUBSPACES
    Direct-sum decomposition;
    Characteristic (eigen) values and charateristic (eigen) vectors;
    Characteristic polynomial and minimal polynomial;
    THe Cayley-Hamilton theorem;
    Diagonal matrices and diagonalization;
    Triangular matrices and triangulation.
  3. CANONICAL FORMS
    Cyclic vectors;
    Matrices over F[x];
    Rational canonical form;
    Jordan form.
  4. INNER PRODUCT SPACES
    Scalar products;
    Orthogonal projections, Gram-Schmidt orthogonalization;
    Orthogonal matrices, symmetric matrices;
    Block matrices, positive definite matrices.
Recommended bibliography:
  1. Kenneth Hoffman and Ray Kunze- Linear Algebra.
  2. Open University- Linear Algebra . (in Hebrew)