Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
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_added_multiple_of_row(0,1,1/3); a
[ 1 7/3 11/3]
[ 3 4 5]
with_col_set_to_multiple_of_col(i, j, s)
Set column i equal to s times column j, returning a new matrix.
EXAMPLES: We change the second column to -3 times the first column.
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: b = a.with_col_set_to_multiple_of_col(1,0,-3); b
[ 0 0 2]
[ 3 -9 5]
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_col_set_to_multiple_of_col(1,0,1/2); a
[ 0 0 2]
[ 3 3/2 5]
with_rescaled_col(i, s, start_row=0)
Replaces i-th col of self by s times i-th col of self, returning new matrix.
EXAMPLES: We rescale the last column of a matrix over the integers:
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: b = a.with_rescaled_col(2,-2); b
[ 0 1 -4]
[ 3 4 -10]
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_col(1,1/3); a
[ 0 1/3 2]
[ 3 4/3 5]
with_rescaled_row(i, s, start_col=0)
Replaces i-th row of self by s times i-th row of self, returning new matrix.
92 Chapter 5. Base class for matrices, part 0