Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[ 3 4 5/2]
sage: R. = QQ[]
We rescale the last column of a matrix over a polynomial ring:
sage: a = matrix(R,2,3,[1,x,x^2,x^3,x^4,x^5]); a
[ 1 x x^2]
[x^3 x^4 x^5]
sage: a.rescale_col(2,1/2); a
[ 1 x 1/2*x^2]
[ x^3 x^4 1/2*x^5]
We try and fail to rescale a matrix over the integers by a non-integer:
sage: a = matrix(ZZ,2,3,[0,1,2, 3,4,4]); a
[0 1 2]
[3 4 4]
sage: a.rescale_col(2,1/2)
Traceback (most recent call last):
...
TypeError: Rescaling column by Rational Field element cannot be done over Integer Ring, use
To rescale the matrix by 1/2, you must change the base ring to the rationals:
sage: a = a.change_ring(QQ); a
[0 1 2]
[3 4 4]
sage: a.rescale_col(2,1/2); a
[0 1 1]
[3 4 2]
rescale_row(i, s, start_col=0)
Replace i-th row of self by s times i-th row of self.
INPUT:
•i - ith row
•s - scalar
•start_col - only rescale entries at this column and to the right
EXAMPLES: We rescale the second row of a matrix over the rational numbers:
sage: a = matrix(QQ,3,range(6)); a
[0 1]
[2 3]
[4 5]
sage: a.rescale_row(1,1/2); a
[ 0 1]
[ 1 3/2]
[ 4 5]
We rescale the second row of a matrix over a polynomial ring:
sage: R. = QQ[]
sage: a = matrix(R,3,[1,x,x^2,x^3,x^4,x^5]);a
[ 1 x]
[x^2 x^3]
[x^4 x^5]
sage: a.rescale_row(1,1/2); a
[ 1 x]
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