Question

I have created a 2×2 matrix of 2×2 matrices:

a = matrix([[matrix([[ 1,  2], [ 3,  4]]),
             matrix([[ 5,  6], [ 7,  8]])],
            [matrix([[ 9, 10], [11, 12]]),
             matrix([[13, 14], [15, 16]])]])

When I multiple it by number (e.g. type a*3) the following error occurs:

TypeError: unsupported operand parent(s) for '*':
           'Full MatrixSpace of 2 by 2 dense matrices over Integer Ring' and
           'Full MatrixSpace of 2 by 2 dense matrices over Integer Ring'

This looks strange because Full MatrixSpace of 2 by 2 dense matrices over Integer Ring is the parent of the sub-matrices (parent(a[0,0])) and I can multiply them without any problem:

sage: a[0,0]*a[0,0]
[ 7 10]
[15 22]

Any of the following commands works fine:

sage: a[0,0]*3
sage: a[0,0]*a[0,0]
sage: a[0,0]*a
sage: a*a
sage: a[0,0]*3*a
sage: diagonal_matrix([3]*2)*a    # I don't want do this every time!

but these do not:

sage: a*3            #TypeError
sage: a[0,0]*a*3     #TypeError

So here are the questions:

1. why it says that multiplication of 2×2 matrices is not supported?
2. why does this multiplication appear when I multiple the matrix by a scalar?
3. can I multiple the matrix by a scalar without the diagonal_matrix cheat?

Answer 1

You’re right that this should work, but as replacements,

sage: (3 * identity_matrix(2)) * a
sage: a * (3 * identity_matrix(2))

both work for me. If you need to do it a lot:

sage: id = identity_matrix(2)
sage: 3 * id * a

You can view this as a bug, or you can view it as a not-yet-implemented feature (combined with a misleading error message). I’ve reported it on the Sage bug tracker.