Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: A.swap_columns(1,2); A
[ 1 -7 9]
[4/5 3 4]
[ 6 3 4]
swap_rows(r1, r2)
Swap rows r1 and r2 of self.
EXAMPLES: We create a rational matrix:
sage: M = MatrixSpace(QQ,3,3)
sage: A = M([1,9,-7,4/5,4,3,6,4,3])
sage: A
[ 1 9 -7]
[4/5 4 3]
[ 6 4 3]
Since the first row is numbered zero, this swaps the first and third rows:
sage: A.swap_rows(0,2); A
[ 6 4 3]
[4/5 4 3]
[ 1 9 -7]
with_added_multiple_of_column(i, j, s, start_row=0)
Add s times column j to column i, returning new matrix.
EXAMPLES: We add -1 times the third column to the second column of an integer matrix, remembering
to start numbering cols at zero:
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: b = a.with_added_multiple_of_column(1,2,-1); b
[ 0 -1 2]
[ 3 -1 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_added_multiple_of_column(0,1,1/3); a
[ 1/3 1 2]
[13/3 4 5]
with_added_multiple_of_row(i, j, s, start_col=0)
Add s times row j to row i, returning new matrix.
EXAMPLES: We add -3 times the first row to the second row of an integer matrix, remembering to start
numbering rows at zero:
sage: a = matrix(ZZ,2,3,range(6)); a
[0 1 2]
[3 4 5]
sage: b = a.with_added_multiple_of_row(1,0,-3); b
[ 0 1 2]
[ 3 1 -1]
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