Sage Reference Manual: Matrices and Spaces of Matrices - Mirrors

Sage Reference Manual: Matrices and Spaces of Matrices, Release 6.1.1
[ 1 1 -1 1 4]
sage: M[3,range(5)]
[-1 2 -2 -1 4]
sage: M[3,:]
[-1 2 -2 -1 4]
sage: M[3,4]
4
sage: M[-1,:]
[-1 2 -2 -1 4]
sage: A = matrix(ZZ,3,4, [3, 2, -5, 0, 1, -1, 1, -4, 1, 0, 1, -3]); A
[ 3 2 -5 0]
[ 1 -1 1 -4]
[ 1 0 1 -3]
A series of three numbers, separated by colons, like n:m:s, means numbers from n up to (but not including) m, in
steps of s. So 0:5:2 means the sequence [0,2,4]:
sage: A[:,0:4:2]
[ 3 -5]
[ 1 1]
[ 1 1]
sage: A[1:,0:4:2]
[1 1]
[1 1]
sage: A[2::-1,:]
[ 1 0 1 -3]
[ 1 -1 1 -4]
[ 3 2 -5 0]
sage: A[1:,3::-1]
[-4 1 -1 1]
[-3 1 0 1]
sage: A[1:,3::-2]
[-4 -1]
[-3 0]
sage: A[2::-1,3:1:-1]
[-3 1]
[-4 1]
[ 0 -5]
We can also change submatrices using these indexing features:
sage: M=matrix([(1, -2, -1, -1,9), (1, 8, 6, 2,2), (1, 1, -1, 1,4), (-1, 2, -2, -1,4)]); M
[ 1 -2 -1 -1 9]
[ 1 8 6 2 2]
[ 1 1 -1 1 4]
[-1 2 -2 -1 4]
Set the 2 x 2 submatrix of M, starting at row index and column index 1:
sage: M[1:3,1:3] = [[1,0],[0,1]]; M
[ 1 -2 -1 -1 9]
3.1. Indexing 61