Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: B.parent()
Full MatrixSpace of 2 by 2 sparse matrices over Rational Field
sage: (A*B).parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
sage: (B*A).parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
sparse_rows(copy=True)
Return a list of the rows of self as sparse vectors (or free module elements).
INPUT:
•copy - (default: True) if True, return a copy so you can modify it safely
EXAMPLES:
sage: m = Mat(ZZ,3,3,sparse=True)(range(9)); m
[0 1 2]
[3 4 5]
[6 7 8]
sage: v = m.sparse_rows(); v
[(0, 1, 2), (3, 4, 5), (6, 7, 8)]
sage: m.sparse_rows(copy=False) is m.sparse_rows(copy=False)
True
sage: v[1].is_sparse()
True
sage: m[0,0] = 10
sage: m.sparse_rows()
[(10, 1, 2), (3, 4, 5), (6, 7, 8)]
TESTS:
Rows of sparse matrices having no rows were fixed on trac ticket #10714:
sage: m = matrix(0, 10, sparse=True)
sage: m.nrows()
0
sage: m.rows()
[]
Check that the returned rows are immutable as per trac ticket #14874:
sage: m = Mat(ZZ,3,3,sparse=True)(range(9))
sage: v = m.sparse_rows()
sage: map(lambda x: x.is_mutable(), v)
[False, False, False]
stack(bottom, subdivide=False)
Returns a new matrix formed by appending the matrix (or vector) bottom beneath self.
INPUT:
•bottom - a matrix, vector or free module element, whose dimensions are compatible with self.
•subdivide - default: False - request the resulting matrix to have a new subdivision, separating
self from bottom.
OUTPUT:
A new matrix formed by appending bottom beneath self. If bottom is a vector (or free module
element) then in this context it is appropriate to consider it as a row vector. (The code first converts a
vector to a 1-row matrix.)
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