Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
If subdivide is True then any row subdivisions for the two matrices are preserved, and a new subdivision
is added between self and bottom. If the column divisions are identical, then they are preserved,
otherwise they are discarded. When subdivide is False there is no subdivision information in the
result.
Warning: If subdivide is True then unequal column subdivisions will be discarded, since it
would be ambiguous how to interpret them. If the subdivision behavior is not what you need, you
can manage subdivisions yourself with methods like subdivisions() and subdivide(). You
might also find block_matrix() or block_diagonal_matrix() useful and simpler in some
instances.
EXAMPLES:
Stacking with a matrix.
sage: A = matrix(QQ, 4, 3, range(12))
sage: B = matrix(QQ, 3, 3, range(9))
sage: A.stack(B)
[ 0 1 2]
[ 3 4 5]
[ 6 7 8]
[ 9 10 11]
[ 0 1 2]
[ 3 4 5]
[ 6 7 8]
Stacking with a vector.
sage: A = matrix(QQ, 3, 2, [0, 2, 4, 6, 8, 10])
sage: v = vector(QQ, 2, [100, 200])
sage: A.stack(v)
[ 0 2]
[ 4 6]
[ 8 10]
[100 200]
Errors are raised if the sizes are incompatible.
sage: A = matrix(RR, [[1, 2],[3, 4]])
sage: B = matrix(RR, [[10, 20, 30], [40, 50, 60]])
sage: A.stack(B)
Traceback (most recent call last):
...
TypeError: number of columns must be the same, 2 != 3
sage: v = vector(RR, [100, 200, 300])
sage: A.stack(v)
Traceback (most recent call last):
...
TypeError: number of columns must be the same, 2 != 3
Setting subdivide to True will, in its simplest form, add a subdivision between self and bottom.
sage: A = matrix(QQ, 2, 5, range(10))
sage: B = matrix(QQ, 3, 5, range(15))
sage: A.stack(B, subdivide=True)
[ 0 1 2 3 4]
[ 5 6 7 8 9]
[--------------]
114 Chapter 6. Base class for matrices, part 1