Trac 15104: Faster creation of transposed matrix' parent

src/sage/matrix/matrix1.pyx

@@ -2206,8 +2206,11 @@ cdef class Matrix(matrix0.Matrix):
             Full MatrixSpace of 2 by 3 dense matrices over Real Field with 53 bits of precision
 
         """
-        if self._nrows == nrows and self._ncols == ncols and (sparse is None or self.is_sparse() == sparse):
-            return self._parent(entries=entries, coerce=coerce, copy=copy)
+        if (sparse is None or self.is_sparse() == sparse):
+            if self._nrows == nrows and self._ncols == ncols:
+                return self._parent(entries=entries, coerce=coerce, copy=copy)
+            elif self._nrows == ncols and self._ncols == nrows:
+                return self._parent.transposed(entries=entries, coerce=coerce, copy=copy)
         return self.matrix_space(nrows, ncols, sparse=sparse)(entries=entries,
                                              coerce=coerce, copy=copy)
     def block_sum(self, Matrix other):

src/sage/matrix/matrix_space.py

@@ -339,6 +339,15 @@ def full_category_initialisation(self):
         self._category_is_initialised = True
         sage.structure.parent.Parent.__init__(self, category=category)
 
+    @lazy_attribute
+    def transposed(self):
+        """
+        The transposed matrix space, having the same base ring and sparseness,
+        but number of columns and rows is swapped.
+
+        """
+        return MatrixSpace(self._base, self.__ncols, self.__nrows, self.__is_sparse)
+
     @lazy_attribute
     def _copy_zero(self):
         """