Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
sage: a.add_multiple_of_row(1,0,-3)
sage: a
[ 0 1 2]
[ 3 1 -1]
To add a rational multiple, we first need to change the base ring:
sage: a = a.change_ring(QQ)
sage: a.add_multiple_of_row(1,0,1/3)
sage: a
[ 0 1 2]
[ 3 4/3 -1/3]
If not, we get an error message:
sage: a.add_multiple_of_row(1,0,i)
Traceback (most recent call last):
...
TypeError: Multiplying row by Symbolic Ring element cannot be done over Rational Field, use
anticommutator(other)
Return the anticommutator self and other.
The anticommutator of two n × n matrices A and B is defined as {A, B} := AB + BA (sometimes this
is written as [A, B] + ).
EXAMPLES:
sage: A = Matrix(ZZ, 2, 2, range(4))
sage: B = Matrix(ZZ, 2, 2, [0, 1, 0, 0])
sage: A.anticommutator(B)
[2 3]
[0 2]
sage: A.anticommutator(B) == B.anticommutator(A)
True
sage: A.commutator(B) + B.anticommutator(A) == 2*A*B
True
base_ring()
Returns the base ring of the matrix.
EXAMPLES:
sage: m=matrix(QQ,2,[1,2,3,4])
sage: m.base_ring()
Rational Field
change_ring(ring)
Return the matrix obtained by coercing the entries of this matrix into the given ring.
Always returns a copy (unless self is immutable, in which case returns self).
EXAMPLES:
sage: A = Matrix(QQ, 2, 2, [1/2, 1/3, 1/3, 1/4])
sage: A.parent()
Full MatrixSpace of 2 by 2 dense matrices over Rational Field
sage: A.change_ring(GF(25,’a’))
[3 2]
[2 4]
sage: A.change_ring(GF(25,’a’)).parent()
71