Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[-----+-----+-----+-]
[0 0 0|0 0 0|0 0 0|3]
sage: T * J * T**(-1) == A
True
sage: T.rank()
10
sage: A = matrix(QQ, [[15, 37/3, -16, -14/3, -29, -7/3, 0, 2/3, 1/3, 44/3], [2, 9, -1, 0, -6
[ 15 37/3 -16 -14/3 -29 -7/3 0 2/3 1/3 44/3]
[ 2 9 -1 0 -6 0 0 0 0 3]
[ 24 74/3 -41 -28/3 -58 -23/3 0 4/3 2/3 88/3]
[ -6 -19 3 3 19 0 0 0 0 -9]
[ 2 6 3 0 -3 1 0 0 0 3]
[ -96 -296/3 176 112/3 232 101/3 0 -16/3 -8/3 -352/3]
[ -4 -2/3 21 16/3 4 14/3 3 -1/3 4/3 -25/3]
[ 20 26/3 -66 -28/3 -42 -41/3 0 13/3 2/3 82/3]
[ 18 57 -9 0 -57 0 0 0 3 28]
[ 0 0 0 0 0 0 0 0 0 3]
sage: J, T = A.jordan_form(transformation=True); J
[3 1 0|0 0 0|0 0|0 0]
[0 3 1|0 0 0|0 0|0 0]
[0 0 3|0 0 0|0 0|0 0]
[-----+-----+---+---]
[0 0 0|3 1 0|0 0|0 0]
[0 0 0|0 3 1|0 0|0 0]
[0 0 0|0 0 3|0 0|0 0]
[-----+-----+---+---]
[0 0 0|0 0 0|3 1|0 0]
[0 0 0|0 0 0|0 3|0 0]
[-----+-----+---+---]
[0 0 0|0 0 0|0 0|3 1]
[0 0 0|0 0 0|0 0|0 3]
sage: T * J * T**(-1) == A
True
sage: T.rank()
10
sage: A = matrix(QQ, [[15, 37/3, -16, -104/3, -29, -7/3, 35, 2/3, -29/3, -1/3], [2, 9, -1, -
[ 15 37/3 -16 -104/3 -29 -7/3 35 2/3 -29/3 -1/3]
[ 2 9 -1 -6 -6 0 7 0 -2 0]
[ 24 74/3 -29 -208/3 -58 -14/3 70 4/3 -58/3 -2/3]
[ -6 -19 3 21 19 0 -21 0 6 0]
[ 2 6 -1 -6 -3 0 7 0 -2 0]
[ -96 -296/3 128 832/3 232 65/3 -279 -16/3 232/3 8/3]
[ 0 0 0 0 0 0 3 0 0 0]
[ 20 26/3 -30 -199/3 -42 -14/3 70 13/3 -55/3 -2/3]
[ 18 57 -9 -54 -57 0 63 0 -15 0]
[ 0 0 0 0 0 0 0 0 0 3]
sage: J, T = A.jordan_form(transformation=True); J
[3 1 0|0 0|0 0|0 0|0]
[0 3 1|0 0|0 0|0 0|0]
[0 0 3|0 0|0 0|0 0|0]
[-----+---+---+---+-]
[0 0 0|3 1|0 0|0 0|0]
[0 0 0|0 3|0 0|0 0|0]
[-----+---+---+---+-]
[0 0 0|0 0|3 1|0 0|0]
[0 0 0|0 0|0 3|0 0|0]
199