+ # Now that everything else is ready, we clobber our computed
+ # matrix basis with the "correct" one consisting of ordered
+ # tuples. Since we didn't orthonormalize our basis, we can
+ # create these from the basis that was handed to us; that is,
+ # we don't need to use the one that the earlier __init__()
+ # method came up with.
+ m = len(self.cartesian_factors())
+ MS = self.matrix_space()
+ self._matrix_basis = tuple(
+ MS(tuple( self.cartesian_projection(i)(b).to_matrix()
+ for i in range(m) ))
+ for b in self.basis()
+ )
+
+ def matrix_space(self):
+ r"""
+ Return the space that our matrix basis lives in as a Cartesian
+ product.
+
+ SETUP::
+
+ sage: from mjo.eja.eja_algebra import (HadamardEJA,
+ ....: RealSymmetricEJA)
+
+ EXAMPLES::
+
+ sage: J1 = HadamardEJA(1)
+ sage: J2 = RealSymmetricEJA(2)
+ sage: J = cartesian_product([J1,J2])
+ sage: J.matrix_space()
+ The Cartesian product of (Full MatrixSpace of 1 by 1 dense
+ matrices over Algebraic Real Field, Full MatrixSpace of 2
+ by 2 dense matrices over Algebraic Real Field)
+
+ """
+ from sage.categories.cartesian_product import cartesian_product
+ return cartesian_product( [J.matrix_space()
+ for J in self.cartesian_factors()] )
+