+ for j in range(i+1) )
+
+
+ def is_skew_symmetric(self):
+ r"""
+ Return whether or not this matrix is skew-symmetric.
+
+ SETUP::
+
+ sage: from mjo.hurwitz import (ComplexMatrixAlgebra,
+ ....: HurwitzMatrixAlgebra)
+
+ EXAMPLES::
+
+ sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+ sage: M = A([ [ 0,I],
+ ....: [-I,1] ])
+ sage: M.is_skew_symmetric()
+ False
+
+ ::
+
+ sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+ sage: M = A([ [ 0, 1+I],
+ ....: [-1-I, 0] ])
+ sage: M.is_skew_symmetric()
+ True
+
+ ::
+
+ sage: A = HurwitzMatrixAlgebra(2, AA, QQ)
+ sage: M = A([ [1, 1],
+ ....: [1, 1] ])
+ sage: M.is_skew_symmetric()
+ False
+
+ ::
+
+ sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+ sage: M = A([ [2*I , 1 + I],
+ ....: [-1 + I, -2*I] ])
+ sage: M.is_skew_symmetric()
+ False
+
+ """
+ # A tiny bit faster than checking equality with the negation
+ # of the transpose.
+ return all( self[i,j] == -self[j,i]
+ for i in range(self.nrows())
+ for j in range(i+1) )