Prof. Yoav Segev

Course Content

  1. Polynomialsalgebras and idealsthe algebra of polynomials and its ideal sturctureLagrange interpolationthe prime factorization of a polynomial.2. Elementary canonical forms characteristic values and vectors of linear transformations and matrices.characteristic polynomials and annihilating polynomialsinvariant subspaces.direct sum decompostions .invariant direct sums. the primary decomposition theorem.diagonalization:necessary and sufficient conditions for diagonilaztion, computing diagonalizing matrices.3. Inner product spacesinner productsinner product spaces linear functionals and adjointsunitary operatorsHermitian operatorsnormal operators and the spectral decomposition theoremsingular value decomposition theorem and applications4. Jordan forms (optional)cyclic subspaces and annihilatorscyclic decompostionsthe Jordan form and its computation

University course catalogue: 201.1.7021

Students' Issues