Interface CStarAlgebra<E,F>

All Superinterfaces:
AbelianGroup<E>, AbelianMonoid<E>, Algebra<E,F>, BanachAlgebra<E,F>, Group<E>, Magma<E>, Module<E,F>, Monoid<E>, Ring<E>, Semiring<E>, Set<E>
public interface CStarAlgebra<E,F> extends BanachAlgebra<E,F>
Represents a C*-algebra (C-star algebra).

A C*-algebra is a Banach algebra with an involution * satisfying: ||x*x|| = ||x||²

C*-algebras are fundamental in quantum mechanics and functional analysis.

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Method Details

    • involution

      E involution(E element)
      Returns the involution (adjoint) of an element. For matrices, this is the conjugate transpose.

    • isSelfAdjoint

      default boolean isSelfAdjoint(E element)
      Checks if an element is self-adjoint (Hermitian): x* = x

    • isNormal

      default boolean isNormal(E element)
      Checks if an element is normal: x*x = xx*

    • isUnitary

      default boolean isUnitary(E element)
      Checks if an element is unitary: x*x = xx* = 1

    • isPositive

      boolean isPositive(E element)
      Checks if an element is positive: x = y*y for some y

    • spectralRadius

      double spectralRadius(E element)
      Returns the spectral radius of an element.