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To get some documentation on how to create custom matrices, you can do:

sage: matrix?

You will

For example, if you want that the entry [i,j] has value i*j^2 (say), you can do:

sage: m = 4 ; n = 5
sage: matrix(QQ, m, n, lambda i, j: i*j^2)
[ 0  0  0  0  0]
[ 0  1  4  9 16]
[ 0  2  8 18 32]
[ 0  3 12 27 48]

To get some documentation on how to create custom matrices, you can do:

sage: matrix?

You will see some examples using a function taking a pair (i,j) and returning some f(i,j) to be placed in the entry [i,j] of the constructed matrix.

For example, if you want that the entry [i,j] has value i*j^2 (say), you can do:

sage: m = 4 ; n = 5
sage: matrix(QQ, m, n, lambda i, j: i*j^2)
[ 0  0  0  0  0]
[ 0  1  4  9 16]
[ 0  2  8 18 32]
[ 0  3 12 27 48]