Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: F = E.augment(B); F
[ 1 2 y y^2]
sage: F.parent()
Full MatrixSpace of 1 by 4 dense matrices over Univariate Polynomial Ring in y over Rational
AUTHORS:
•Naqi Jaffery (2006-01-24): examples
•Rob Beezer (2010-12-07): vector argument, docstring, subdivisions
block_sum(other)
Return the block matrix that has self and other on the diagonal:
[ self 0 ]
[ 0 other ]
EXAMPLES:
sage: A = matrix(QQ[[’t’]], 2, range(1, 5))
sage: A.block_sum(100*A)
[ 1 2 0 0]
[ 3 4 0 0]
[ 0 0 100 200]
[ 0 0 300 400]
column(i, from_list=False)
Return the i‘th column of this matrix as a vector.
This column is a dense vector if and only if the matrix is a dense matrix.
INPUT:
•i - integer
•from_list - bool (default: False); if true, returns the i‘th element of self.columns() (see
columns()), which may be faster, but requires building a list of all columns the first time it is called
after an entry of the matrix is changed.
EXAMPLES:
sage: a = matrix(2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a.column(1)
(1, 4)
If the column is negative, it wraps around, just like with list indexing, e.g., -1 gives the right-most column:
sage: a.column(-1)
(2, 5)
TESTS:
sage: a = matrix(2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a.column(3)
Traceback (most recent call last):
...
IndexError: column index out of range
sage: a.column(-4)
100 Chapter 6. Base class for matrices, part 1