Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[1||2 3]
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matrix_from_columns(cols)
Return the matrix constructed from self using columns with indices in the columns list.
EXAMPLES:
sage: M = MatrixSpace(GF(127),3,3,sparse=True)
sage: A = M(range(9)); A
[0 1 2]
[3 4 5]
[6 7 8]
sage: A.matrix_from_columns([2,1])
[2 1]
[5 4]
[8 7]
matrix_from_rows(rows)
Return the matrix constructed from self using rows with indices in the rows list.
p
INPUT:
•rows - list or tuple of row indices
EXAMPLE:
sage: M = MatrixSpace(GF(127),3,3,sparse=True)
sage: A = M(range(9)); A
[0 1 2]
[3 4 5]
[6 7 8]
sage: A.matrix_from_rows([2,1])
[6 7 8]
[3 4 5]
rank(gauss=False)
Compute the rank of self.
INPUT:
•gauss - if True LinBox’ Gaussian elimination is used. If False ‘Symbolic Reordering’ as implemented
in LinBox is used. If ‘native’ the native Sage implementation is used. (default: False)
EXAMPLE:
sage: A = random_matrix(GF(127),200,200,density=0.01,sparse=True)
sage: r1 = A.rank(gauss=False)
sage: r2 = A.rank(gauss=True)
sage: r3 = A.rank(gauss=’native’)
sage: r1 == r2 == r3
True
sage: r1
155
ALGORITHM: Uses LinBox or native implementation.
REFERENCES:
301