Symmetric operator

Dependencies:

  1. Linear transformation
  2. Inner product space

Let L:VV be a linear transformation over an inner product space.

L is a symmetric operator iff (u,vV,L(u),v=u,L(v)).

Dependency for:

  1. Symmetric operator iff hermitian
  2. Symmetric operator on V has a basis of orthonormal eigenvectors
  3. All eigenvalues of a symmetric operator are real

Info:

Transitive dependencies:

  1. Group
  2. Ring
  3. Field
  4. Vector Space
  5. Linear transformation
  6. Inner product space