Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: R.=GF(3)[]
sage: A = matrix(GF(3),2,[0,0,1,2])
sage: A.minpoly()
x^2 + x
Minpoly with proof=False is dramatically (“millions” of times!) faster than minpoly with proof=True.
This matters since proof=True is the default, unless you first type ‘’proof.linear_algebra(False)’‘.:
sage: A.minpoly(proof=False) in [x, x+1, x^2+x]
True
randomize(density=1, nonzero=False)
Randomize density proportion of the entries of this matrix, leaving the rest unchanged.
INPUT:
•density - Integer; proportion (roughly) to be considered for changes
•nonzero - Bool (default: False); whether the new entries are forced to be non-zero
OUTPUT:
•None, the matrix is modified in-space
EXAMPLES:
sage: A = matrix(GF(5), 5, 5, 0)
sage: A.randomize(0.5); A
[0 0 0 2 0]
[0 3 0 0 2]
[4 0 0 0 0]
[4 0 0 0 0]
[0 1 0 0 0]
sage: A.randomize(); A
[3 3 2 1 2]
[4 3 3 2 2]
[0 3 3 3 3]
[3 3 2 2 4]
[2 2 2 1 4]
rank()
Return the rank of this matrix.
EXAMPLES:
sage: m = matrix(GF(7),5,range(25))
sage: m.rank()
2
Rank is not implemented over the integers modulo a composite yet.:
sage: m = matrix(Integers(4), 2, [2,2,2,2])
sage: m.rank()
Traceback (most recent call last):
...
NotImplementedError: Echelon form not implemented over ’Ring of integers modulo 4’.
sage.matrix.matrix_modn_dense.is_Matrix_modn_dense(self )
297