Symmetric operator

Dependencies:

1. Linear transformation
2. Inner product space

Let $L: V \mapsto V$ be a linear transformation over an inner product space.

$L$ is a symmetric operator iff $(\forall u, v \in V, \langle L(u), v \rangle = \langle u, L(v) \rangle)$.

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:

• Depth: 5
• Number of transitive dependencies: 6

Transitive dependencies:

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