Trait SelfAdjointOperator 

pub trait SelfAdjointOperator<V, S = SelfAdjoint>: LinearOperator<V, V>
where
    S: SymmetryProperty,
{
    // Required method
    fn quadratic_form(&self, x: &V) -> Result<f64>;

    // Provided methods
    fn has_real_spectrum(&self) -> bool { ... }
    fn is_positive(&self, x: &V) -> Result<bool> { ... }
    fn is_positive_definite(&self, x: &V, tolerance: f64) -> Result<bool> { ... }
}

A self-adjoint operator (T = T*).

Self-adjoint operators have:

• Real spectrum
• Orthogonal eigenvectors
• Spectral decomposition

Type Parameters

• V - The Hilbert space element type
• S - Symmetry phantom marker (should be SelfAdjoint)

Required Methods

fn quadratic_form(&self, x: &V) -> Result<f64>

Compute the quadratic form ⟨Tx, x⟩.

Provided Methods

fn has_real_spectrum(&self) -> bool

Check if all eigenvalues are real (always true for self-adjoint).

fn is_positive(&self, x: &V) -> Result<bool>

Check if the operator is positive (⟨Tx, x⟩ ≥ 0).

fn is_positive_definite(&self, x: &V, tolerance: f64) -> Result<bool>

Check if the operator is positive definite (⟨Tx, x⟩ > 0 for x ≠ 0).

Implementors