Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
•i - integer
•from_list - bool (default: False); if true, returns the i‘th element of self.rows() (see
rows()), which may be faster, but requires building a list of all rows 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.row(0)
(0, 1, 2)
sage: a.row(1)
(3, 4, 5)
sage: a.row(-1) # last row
(3, 4, 5)
TESTS:
sage: a = matrix(2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a.row(2)
Traceback (most recent call last):
...
IndexError: row index out of range
sage: a.row(-3)
Traceback (most recent call last):
...
IndexError: row index out of range
rows(copy=True)
Return a list of the rows of self.
INPUT:
•copy - (default: True) if True, return a copy of the list of rows which is safe to change.
If self is a sparse matrix, rows are returned as sparse vectors, otherwise returned vectors are dense.
EXAMPLES:
sage: matrix(3, [1..9]).rows()
[(1, 2, 3), (4, 5, 6), (7, 8, 9)]
sage: matrix(RR, 2, [sqrt(2), pi, exp(1), 0]).rows()
[(1.41421356237310, 3.14159265358979), (2.71828182845905, 0.000000000000000)]
sage: matrix(RR, 0, 2, []).rows()
[]
sage: matrix(RR, 2, 0, []).rows()
[(), ()]
sage: m = matrix(RR, 3, 3, {(1,2): pi, (2, 2): -1, (0,1): sqrt(2)})
sage: parent(m.rows()[0])
Sparse vector space of dimension 3 over Real Field with 53 bits of precision
Sparse matrices produce sparse rows.
sage: A = matrix(QQ, 2, range(4), sparse=True)
sage: v = A.rows()[0]
sage: v.is_sparse()
True
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