Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
otherwise they are discarded. When subdivide is False there is no subdivision information in the
result.
Warning: If subdivide is True then unequal row 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 get_subdivisions() and subdivide(). You
might also find block_matrix() or block_diagonal_matrix() useful and simpler in some
instances.
EXAMPLES:
Augmenting with a matrix.
sage: A = matrix(QQ, 3, range(12))
sage: B = matrix(QQ, 3, range(9))
sage: A.augment(B)
[ 0 1 2 3 0 1 2]
[ 4 5 6 7 3 4 5]
[ 8 9 10 11 6 7 8]
Augmenting with a vector.
sage: A = matrix(QQ, 2, [0, 2, 4, 6, 8, 10])
sage: v = vector(QQ, 2, [100, 200])
sage: A.augment(v)
[ 0 2 4 100]
[ 6 8 10 200]
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.augment(B)
Traceback (most recent call last):
...
TypeError: number of rows must be the same, 2 != 3
sage: v = vector(RR, [100, 200, 300])
sage: A.augment(v)
Traceback (most recent call last):
...
TypeError: number of rows must be the same, 2 != 3
Setting subdivide to True will, in its simplest form, add a subdivision between self and right.
sage: A = matrix(QQ, 3, range(12))
sage: B = matrix(QQ, 3, range(15))
sage: A.augment(B, subdivide=True)
[ 0 1 2 3| 0 1 2 3 4]
[ 4 5 6 7| 5 6 7 8 9]
[ 8 9 10 11|10 11 12 13 14]
Column subdivisions are preserved by augmentation, and enriched, if subdivisions are requested. (So
multiple augmentations can be recorded.)
sage: A = matrix(QQ, 3, range(6))
sage: A.subdivide(None, [1])
sage: B = matrix(QQ, 3, range(9))
sage: B.subdivide(None, [2])
sage: A.augment(B, subdivide=True)
98 Chapter 6. Base class for matrices, part 1