From: Michael Orlitzky <michael@orlitzky.com>
Date: Tue, 2 Mar 2021 16:14:30 +0000 (-0500)
Subject: octonions: add is_hermitian() for octonion matrices.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=9ffb2ed473d62df9f6b6db9636b0bf8fa8f3be25;p=sage.d.git

octonions: add is_hermitian() for octonion matrices.
---

diff --git a/mjo/octonions.py b/mjo/octonions.py
index 73acf2d..87bf5ff 100644
--- a/mjo/octonions.py
+++ b/mjo/octonions.py
@@ -463,6 +463,23 @@ class OctonionMatrix(IndexedFreeModuleElement):
         """
         return self.parent()
 
+    def is_hermitian(self):
+        r"""
+
+        SETUP::
+
+            sage: from mjo.octonions import OctonionMatrixAlgebra
+
+        EXAMPLES::
+
+            sage: MS = OctonionMatrixAlgebra(3)
+            sage: MS.one().is_hermitian()
+            True
+
+        """
+        return all( self[i,j] == self[j,i].conjugate()
+                    for i in range(self.nrows())
+                    for j in range(self.ncols()) )
 
 class OctonionMatrixAlgebra(CombinatorialFreeModule):
     r"""