Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
EXAMPLES:
sage: A = M([1,2,3,4,5,6,7, 22,3/4,34,11,7,5,3, 99,65,1/2,2/3,3/5,4/5,5/6, 9,8/9, 9/8,7/6,6/
sage: M = MatrixSpace(QQ,6,7)
sage: A
[ 1 2 3 4 5 6 7]
[ 22 3/4 34 11 7 5 3]
[ 99 65 1/2 2/3 3/5 4/5 5/6]
[ 9 8/9 9/8 7/6 6/7 76 4]
[ 0 9 8 7 6 5 4]
[ 123 99 91 28 6 1024 1]
sage: A.ncols()
7
sage: A.nrows()
6
AUTHORS:
•Naqi Jaffery (2006-01-24): examples
pivots()
Return the pivot column positions of this matrix.
OUTPUT: a tuple of Python integers: the position of the first nonzero entry in each row of the echelon
form.
This returns a tuple so it is immutable; see #10752.
EXAMPLES:
sage: A = matrix(QQ, 2, 2, range(4))
sage: A.pivots()
(0, 1)
rank()
TESTS:
We should be able to compute the rank of a matrix whose entries are polynomials over a finite field (trac
#5014):
sage: P. = PolynomialRing(GF(17))
sage: m = matrix(P, [ [ 6*x^2 + 8*x + 12, 10*x^2 + 4*x + 11],
... [8*x^2 + 12*x + 15, 8*x^2 + 9*x + 16] ])
sage: m.rank()
2
rescale_col(i, s, start_row=0)
Replace i-th col of self by s times i-th col of self.
INPUT:
•i - ith column
•s - scalar
•start_row - only rescale entries at this row and lower
EXAMPLES: We rescale the last column of a matrix over the rational numbers:
sage: a = matrix(QQ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: a.rescale_col(2,1/2); a
[ 0 1 1]
86 Chapter 5. Base class for matrices, part 0