Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
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sage: TestSuite(a).run()
sage: TestSuite(b).run()
sage: a.echelonize(); a
[1 0 0]
[0 1 0]
[0 0 1]
sage: b.echelonize(); b
[ 1 0 36]
[ 0 1 2]
We create a matrix group:
sage: M = MatrixSpace(GF(3),3,3)
sage: G = MatrixGroup([M([[0,1,0],[0,0,1],[1,0,0]]), M([[0,1,0],[1,0,0],[0,0,1]])])
sage: G
Matrix group over Finite Field of size 3 with 2 generators (
[0 1 0] [0 1 0]
[0 0 1] [1 0 0]
[1 0 0], [0 0 1]
)
sage: G.gap()
Group([ [ [ 0*Z(3), Z(3)^0, 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3)^0 ], [ Z(3)^0, 0*Z(3), 0*Z(3) ] ],
[ [ 0*Z(3), Z(3)^0, 0*Z(3) ], [ Z(3)^0, 0*Z(3), 0*Z(3) ], [ 0*Z(3), 0*Z(3), Z(3)^0 ] ] ])
TESTS:
sage: M = MatrixSpace(GF(5),2,2)
sage: A = M([1,0,0,1])
sage: A - int(-1)
[2 0]
[0 2]
sage: B = M([4,0,0,1])
sage: B - int(-1)
[0 0]
[0 2]
sage: Matrix(GF(5),0,0, sparse=False).inverse()
[]
class sage.matrix.matrix_modn_dense.Matrix_modn_dense
Bases: sage.matrix.matrix_dense.Matrix_dense
TESTS:
sage: matrix(GF(7), 2, 2, [-1, int(-2), GF(7)(-3), 1/4])
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[4 2]
charpoly(var=’x’, algorithm=’generic’)
Returns the characteristic polynomial of self.
INPUT:
•var - a variable name
•algorithm - ‘generic’ (default)
EXAMPLES:
294 Chapter 14. Dense matrices over Z/nZ for n small