Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
EXAMPLES:
sage: matrix(QQ,2,2,range(4)).is_sparse()
False
sage: matrix(QQ,2,2,range(4),sparse=True).is_sparse()
True
is_square()
Return True precisely if this matrix is square, i.e., has the same number of rows and columns.
EXAMPLES:
sage: matrix(QQ,2,2,range(4)).is_square()
True
sage: matrix(QQ,2,3,range(6)).is_square()
False
is_symmetric()
Returns True if this is a symmetric matrix.
EXAMPLES:
sage: m=Matrix(QQ,2,range(0,4))
sage: m.is_symmetric()
False
sage: m=Matrix(QQ,2,(1,1,1,1,1,1))
sage: m.is_symmetric()
False
sage: m=Matrix(QQ,1,(2,))
sage: m.is_symmetric()
True
is_symmetrizable(return_diag=False, positive=True)
This function takes a square matrix over an ordered integral domain and checks if it is symmetrizable. A
matrix B is symmetrizable iff there exists an invertible diagonal matrix D such that DB is symmetric.
Warning: Expects self to be a matrix over an ordered integral domain.
INPUT:
•return_diag – bool(default:False) if True and self is symmetrizable the diagonal entries of the
matrix D are returned.
•positive – bool(default:True) if True, the condition that D has positive entries is added.
OUTPUT:
•True – if self is symmetrizable and return_diag is False
•the diagonal entries of a matrix D such that DB is symmetric – iff self is symmetrizable and
return_diag is True
•False – iff self is not symmetrizable
EXAMPLES:
sage: matrix([[0,6],[3,0]]).is_symmetrizable(positive=False)
True
sage: matrix([[0,6],[3,0]]).is_symmetrizable(positive=True)
78 Chapter 5. Base class for matrices, part 0