Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
REFERENCES:
•[FZ2001] S. Fomin, A. Zelevinsky. Cluster Algebras 1: Foundations, arXiv:math/0104151 (2001).
ncols()
Return the number of columns of this matrix.
EXAMPLES:
sage: M = MatrixSpace(QQ, 2, 3)
sage: A = M([1,2,3, 4,5,6])
sage: A
[1 2 3]
[4 5 6]
sage: A.ncols()
3
sage: A.nrows()
2
AUTHORS:
•Naqi Jaffery (2006-01-24): examples
nonpivots()
Return the list of i such that the i-th column of self is NOT a pivot column of the reduced row echelon
form of self.
OUTPUT: sorted tuple of (Python) integers
EXAMPLES:
sage: a = matrix(QQ,3,3,range(9)); a
[0 1 2]
[3 4 5]
[6 7 8]
sage: a.echelon_form()
[ 1 0 -1]
[ 0 1 2]
[ 0 0 0]
sage: a.nonpivots()
(2,)
nonzero_positions(copy=True, column_order=False)
Returns the sorted list of pairs (i,j) such that self[i,j] != 0.
INPUT:
•copy - (default: True) It is safe to change the resulting list (unless you give the option copy=False).
•column_order - (default: False) If true, returns the list of pairs (i,j) such that self[i,j] != 0, but
sorted by columns, i.e., column j=0 entries occur first, then column j=1 entries, etc.
EXAMPLES:
sage: a = matrix(QQ, 2,3, [1,2,0,2,0,0]); a
[1 2 0]
[2 0 0]
sage: a.nonzero_positions()
[(0, 0), (0, 1), (1, 0)]
sage: a.nonzero_positions(copy=False)
[(0, 0), (0, 1), (1, 0)]
sage: a.nonzero_positions(column_order=True)
[(0, 0), (1, 0), (0, 1)]
84 Chapter 5. Base class for matrices, part 0