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40f0571)
We only need to test these above and on the diagonal.
sage: M.is_hermitian()
True
sage: M.is_hermitian()
True
+ ::
+
+ sage: A = ComplexMatrixAlgebra(2, QQbar, ZZ)
+ sage: M = A([ [ 0,0],
+ ....: [-I,0] ])
+ sage: M.is_hermitian()
+ False
+
::
sage: A = HurwitzMatrixAlgebra(2, AA, QQ)
::
sage: A = HurwitzMatrixAlgebra(2, AA, QQ)
# transpose.
return all( self[i,j] == self[j,i].conjugate()
for i in range(self.nrows())
# transpose.
return all( self[i,j] == self[j,i].conjugate()
for i in range(self.nrows())
- for j in range(self.ncols()) )
def is_skew_symmetric(self):
def is_skew_symmetric(self):
# of the transpose.
return all( self[i,j] == -self[j,i]
for i in range(self.nrows())
# of the transpose.
return all( self[i,j] == -self[j,i]
for i in range(self.nrows())
- for j in range(self.ncols()) )
class HurwitzMatrixAlgebra(MatrixAlgebra):
class HurwitzMatrixAlgebra(MatrixAlgebra):