mjo: rename matrix_vector.py to basis_repr.py.

[sage.d.git] / mjo / basis_repr.py

diff --git a/mjo/matrix_vector.py b/mjo/basis_repr.py
similarity index 91%
rename from mjo/matrix_vector.py
rename to mjo/basis_repr.py
index 08743d5c5ecf000dbcc5ca6f4b475cd67af6a593..5c85998955ff77f00ff100e3c53f33157e5dec0d 100644 (file)
--- a/mjo/matrix_vector.py
+++ b/mjo/basis_repr.py
@@ -1,9 +1,13 @@
-"""
-There is an explicit isomorphism between all finite-dimensional vector
-spaces. In particular, there is an isomorphism between the m-by-n
-matrices and `$R^(m \times n)$`. Since most vector operations are not
-available on Sage matrices, we have to go back and forth between these
-two vector spaces often.
+r"""
+In an `n`-dimensional vector space, representation with respect to
+a basis is an isometry between that space and `\mathbb{R}^{n}`.
+
+Sage is able to go back/forth relatively easy when you start with a
+``VectorSpace``, but unfortunately, it does not know that a
+``MatrixSpace`` is also a ``VectorSpace``. So, this module exists to
+perform the "basis representation" isometry between a matrix space and
+a vector space of the same dimension.
+
 """
 
 from sage.all import *
@@ -46,7 +50,7 @@ def basis_repr(M):
 
     SETUP::
 
-        sage: from mjo.matrix_vector import basis_repr
+        sage: from mjo.basis_repr import basis_repr
 
     EXAMPLES:
 
@@ -153,8 +157,8 @@ def basis_repr_of_operator(M, L):
 
     SETUP::
 
-        sage: from mjo.matrix_vector import (basis_repr,
-        ....:                                basis_repr_of_operator)
+        sage: from mjo.basis_repr import (basis_repr,
+        ....:                             basis_repr_of_operator)
 
     EXAMPLES: