Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
We can use the step feature of slices to set every other column:
sage: A[:,0:3:2] = 5; A
[ 5 2 5 0]
[ 5 -1 5 -4]
[ 5 0 5 -3]
sage: A[1:,0:4:2] = [[100,200],[300,400]]; A
[ 5 2 5 0]
[100 -1 200 -4]
[300 0 400 -3]
We can also count backwards to flip the matrix upside down:
sage: A[::-1,:]=A; A
[300 0 400 -3]
[100 -1 200 -4]
[ 5 2 5 0]
sage: A[1:,3::-1]=[[2,3,0,1],[9,8,7,6]]; A
[300 0 400 -3]
[ 1 0 3 2]
[ 6 7 8 9]
sage: A[1:,::-2] = A[1:,::2]; A
[300 0 400 -3]
[ 1 3 3 1]
[ 6 8 8 6]
sage: A[::-1,3:1:-1] = [[4,3],[1,2],[-1,-2]]; A
[300 0 -2 -1]
[ 1 3 2 1]
[ 6 8 3 4]
We save and load a matrix:
sage: A = matrix(Integers(8),3,range(9))
sage: loads(dumps(A)) == A
True
MUTABILITY: Matrices are either immutable or not. When initially created, matrices are typically mutable, so
one can change their entries. Once a matrix A is made immutable using A.set_immutable() the entries of A
cannot be changed, and A can never be made mutable again. However, properties of A such as its rank, characteristic
polynomial, etc., are all cached so computations involving A may be more efficient. Once A is made immutable it
cannot be changed back. However, one can obtain a mutable copy of A using copy(A).
EXAMPLES:
sage: A = matrix(RR,2,[1,10,3.5,2])
sage: A.set_immutable()
sage: copy(A) is A
False
The echelon form method always returns immutable matrices with known rank.
EXAMPLES:
sage: A = matrix(Integers(8),3,range(9))
sage: A.determinant()
0
3.1. Indexing 63