X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Fhurwitz.py;h=1f7c9dc3781a844d6d77a1e63168c52340bf6770;hp=ccc8219b1a92036c6ac92f118339c160a885977b;hb=fc29add6cf1d9ff4e8a240b0f8f2ca6672d4ea57;hpb=9861c4860c4bb1158243c06544cb54d1d9e3b411

diff --git a/mjo/hurwitz.py b/mjo/hurwitz.py
index ccc8219..1f7c9dc 100644
--- a/mjo/hurwitz.py
+++ b/mjo/hurwitz.py
@@ -306,6 +306,31 @@ class Octonions(CombinatorialFreeModule):
 
 
 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"""
 
@@ -322,6 +347,8 @@ class HurwitzMatrixAlgebraElement(MatrixAlgebraElement):
             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()) )