Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
Full MatrixSpace of 2 by 2 dense matrices over Finite Field in a of size 5^2
sage: A.change_ring(ZZ)
Traceback (most recent call last):
...
TypeError: matrix has denominators so can’t change to ZZ.
Changing rings preserves subdivisions:
sage: A.subdivide([1], []); A
[1/2 1/3]
[-------]
[1/3 1/4]
sage: A.change_ring(GF(25,’a’))
[3 2]
[---]
[2 4]
commutator(other)
Return the commutator self*other - other*self.
EXAMPLES:
sage: A = Matrix(ZZ, 2, 2, range(4))
sage: B = Matrix(ZZ, 2, 2, [0, 1, 0, 0])
sage: A.commutator(B)
[-2 -3]
[ 0 2]
sage: A.commutator(B) == -B.commutator(A)
True
dict()
Dictionary of the elements of self with keys pairs (i,j) and values the nonzero entries of self.
It is safe to change the returned dictionary.
EXAMPLES:
sage: R. = QQ[]
sage: a = matrix(R,2,[x,y,0, 0,0,2*x+y]); a
[ x y 0]
[ 0 0 2*x + y]
sage: d = a.dict(); d
{(0, 1): y, (1, 2): 2*x + y, (0, 0): x}
Notice that changing the returned list does not change a (the list is a copy):
sage: d[0,0] = 25
sage: a
[ x y 0]
[ 0 0 2*x + y]
dimensions()
Returns the dimensions of this matrix as the tuple (nrows, ncols).
EXAMPLES:
sage: M = matrix([[1,2,3],[4,5,6]])
sage: N = M.transpose()
sage: M.dimensions()
(2, 3)
72 Chapter 5. Base class for matrices, part 0