Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: A = matrix(ZZ, 4, 10, range(40)); A
[ 0 1 2 3 4 5 6 7 8 9]
[10 11 12 13 14 15 16 17 18 19]
[20 21 22 23 24 25 26 27 28 29]
[30 31 32 33 34 35 36 37 38 39]
sage: E = elementary_matrix(4, row1=1, row2=3); E
[1 0 0 0]
[0 0 0 1]
[0 0 1 0]
[0 1 0 0]
sage: E*A
[ 0 1 2 3 4 5 6 7 8 9]
[30 31 32 33 34 35 36 37 38 39]
[20 21 22 23 24 25 26 27 28 29]
[10 11 12 13 14 15 16 17 18 19]
sage: E = elementary_matrix(4, row1=2, scale=10); E
[ 1 0 0 0]
[ 0 1 0 0]
[ 0 0 10 0]
[ 0 0 0 1]
sage: E*A
[ 0 1 2 3 4 5 6 7 8 9]
[ 10 11 12 13 14 15 16 17 18 19]
[200 210 220 230 240 250 260 270 280 290]
[ 30 31 32 33 34 35 36 37 38 39]
sage: E = elementary_matrix(4, row1=2, row2=1, scale=10); E
[ 1 0 0 0]
[ 0 1 0 0]
[ 0 10 1 0]
[ 0 0 0 1]
sage: E*A
[ 0 1 2 3 4 5 6 7 8 9]
[ 10 11 12 13 14 15 16 17 18 19]
[120 131 142 153 164 175 186 197 208 219]
[ 30 31 32 33 34 35 36 37 38 39]
Over the rationals, now as column operations. Recall that row and column numbering begins at zero. Checks
now have the elementary matrix on the right.
sage: A = matrix(QQ, 5, 4, range(20)); A
[ 0 1 2 3]
[ 4 5 6 7]
[ 8 9 10 11]
[12 13 14 15]
[16 17 18 19]
sage: E = elementary_matrix(QQ, 4, col1=1, col2=3); E
[1 0 0 0]
[0 0 0 1]
[0 0 1 0]
[0 1 0 0]
sage: A*E
[ 0 3 2 1]
[ 4 7 6 5]
[ 8 11 10 9]
32 Chapter 2. Matrix Constructor