class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
+ def conjugate_transpose(self):
+ r"""
+ Return the conjugate-transpose of this matrix.
+
+ SETUP::
+
+ sage: from mjo.hurwitz import HurwitzMatrixAlgebra
+
+ EXAMPLES::
+
+ sage: A = HurwitzMatrixAlgebra(2, QQbar, ZZ)
+ sage: M = A([ [ I, 2*I],
+ ....: [ 3*I, 4*I] ])
+ +------+------+
+ | -1*I | -3*I |
+ +------+------+
+ | -2*I | -4*I |
+ +------+------+
+
+ """
+ entries = [ [ self[j,i].conjugate()
+ for j in range(self.ncols())]
+ for i in range(self.nrows()) ]
+ return self.parent()._element_constructor_(entries)
+
def is_hermitian(self):
r"""
True
"""
+ # A tiny bit faster than checking equality with the conjugate
+ # transpose.
return all( self[i,j] == self[j,i].conjugate()
for i in range(self.nrows())
for j in range(self.ncols()) )
+---------------------+
| 1.00000000000000*e0 |
+---------------------+
+ sage: A.gens()
+ (+---------------------+
+ | 1.00000000000000*e0 |
+ +---------------------+,
+ +---------------------+
+ | 1.00000000000000*e1 |
+ +---------------------+,
+ +---------------------+
+ | 1.00000000000000*e2 |
+ +---------------------+,
+ +---------------------+
+ | 1.00000000000000*e3 |
+ +---------------------+,
+ +---------------------+
+ | 1.00000000000000*e4 |
+ +---------------------+,
+ +---------------------+
+ | 1.00000000000000*e5 |
+ +---------------------+,
+ +---------------------+
+ | 1.00000000000000*e6 |
+ +---------------------+,
+ +---------------------+
+ | 1.00000000000000*e7 |
+ +---------------------+)
::
+-----+
| 1.0 |
+-----+
+ sage: A.gens()
+ (+-----+
+ | 1.0 |
+ +-----+,
+ +---+
+ | i |
+ +---+,
+ +---+
+ | j |
+ +---+,
+ +---+
+ | k |
+ +---+)
::
+------------------+
| 1.00000000000000 |
+------------------+
+ sage: A.gens()
+ (+------------------+
+ | 1.00000000000000 |
+ +------------------+,
+ +--------------------+
+ | 1.00000000000000*I |
+ +--------------------+)
::