return (self + (-other))
+ def is_self_adjoint(self):
+ r"""
+ Return whether or not this operator is self-adjoint.
+
+ At least in Sage, the fact that the base field is real means
+ that the algebra elements have to be real as well (this is why
+ we embed the complex numbers and quaternions). As a result, the
+ matrix of this operator will contain only real entries, and it
+ suffices to check only symmetry, not conjugate symmetry.
+
+ SETUP::
+
+ sage: from mjo.eja.eja_algebra import (JordanSpinEJA)
+
+ EXAMPLES::
+
+ sage: J = JordanSpinEJA(4)
+ sage: J.one().operator().is_self_adjoint()
+ True
+
+ """
+ return self.matrix().is_symmetric()
+
+
+ def is_zero(self):
+ r"""
+ Return whether or not this map is the zero operator.
+
+ SETUP::
+
+ sage: from mjo.eja.eja_operator import FiniteDimensionalEuclideanJordanAlgebraOperator
+ sage: from mjo.eja.eja_algebra import (random_eja,
+ ....: JordanSpinEJA,
+ ....: RealSymmetricEJA)
+
+ EXAMPLES::
+
+ sage: J1 = JordanSpinEJA(2)
+ sage: J2 = RealSymmetricEJA(2)
+ sage: R = J1.base_ring()
+ sage: M = matrix(R, [ [0, 0],
+ ....: [0, 0],
+ ....: [0, 0] ])
+ sage: L = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J2,M)
+ sage: L.is_zero()
+ True
+ sage: M = matrix(R, [ [0, 0],
+ ....: [0, 1],
+ ....: [0, 0] ])
+ sage: L = FiniteDimensionalEuclideanJordanAlgebraOperator(J1,J2,M)
+ sage: L.is_zero()
+ False
+
+ TESTS:
+
+ The left-multiplication-by-zero operation on a given algebra
+ is its zero map::
+
+ sage: set_random_seed()
+ sage: J = random_eja()
+ sage: J.zero().operator().is_zero()
+ True
+
+ """
+ return self.matrix().is_zero()
+
+
def inverse(self):
"""
Return the inverse of this operator, if it exists.