Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: m = Mat(ZZ,3,3)(range(9))
sage: v = m.dense_columns()
sage: map(lambda x: x.is_mutable(), v)
[False, False, False]
dense_matrix()
If this matrix is sparse, return a dense matrix with the same entries. If this matrix is dense, return this
matrix (not a copy).
Note: The definition of “dense” and “sparse” in Sage have nothing to do with the number of nonzero
entries. Sparse and dense are properties of the underlying representation of the matrix.
EXAMPLES:
sage: A = MatrixSpace(QQ,2, sparse=True)([1,2,0,1])
sage: A.is_sparse()
True
sage: B = A.dense_matrix()
sage: B.is_sparse()
False
sage: A*B
[1 4]
[0 1]
sage: A.parent()
Full MatrixSpace of 2 by 2 sparse matrices over Rational Field
sage: B.parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
In Sage, the product of a sparse and a dense matrix is always dense:
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
TESTS:
Make sure that subdivisions are preserved when switching between dense and sparse matrices:
sage: a = matrix(ZZ, 3, range(9))
sage: a.subdivide([1,2],2)
sage: a.subdivisions()
([1, 2], [2])
sage: b = a.sparse_matrix().dense_matrix()
sage: b.subdivisions()
([1, 2], [2])
dense_rows(copy=True)
Return list of the dense rows of self.
INPUT:
•copy - (default: True) if True, return a copy so you can modify it safely (note that the individual
vectors in the copy should not be modified since they are mutable!)
EXAMPLES:
sage: m = matrix(3, range(9)); m
[0 1 2]
104 Chapter 6. Base class for matrices, part 1