Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
EXAMPLES: We rescale the second row of a matrix over the integers:
sage: a = matrix(ZZ,3,2,range(6)); a
[0 1]
[2 3]
[4 5]
sage: b = a.with_rescaled_row(1,-2); b
[ 0 1]
[-4 -6]
[ 4 5]
The original matrix is unchanged:
sage: a
[0 1]
[2 3]
[4 5]
Adding a rational multiple is okay, and reassigning a variable is okay:
sage: a = a.with_rescaled_row(2,1/3); a
[ 0 1]
[ 2 3]
[4/3 5/3]
with_row_set_to_multiple_of_row(i, j, s)
Set row i equal to s times row j, returning a new matrix.
EXAMPLES: We change the second row to -3 times the first row:
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: b = a.with_row_set_to_multiple_of_row(1,0,-3); b
[ 0 1 2]
[ 0 -3 -6]
Note that the original matrix is unchanged:
sage: a
[0 1 2]
[3 4 5]
Adding a rational multiple is okay, and reassigning a variable is okay:
sage: a = a.with_row_set_to_multiple_of_row(1,0,1/2); a
[ 0 1 2]
[ 0 1/2 1]
with_swapped_columns(c1, c2)
Swap columns c1 and c2 of self and return a new matrix.
INPUT:
•c1, c2 - integers specifying columns of self to interchange
OUTPUT:
A new matrix, identical to self except that columns c1 and c2 are swapped.
EXAMPLES:
Remember that columns are numbered starting from zero.
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