[Easy question] Dimension of kernel of matrix over Galois field

[Theo Sandstrom]

Hi all,

I am very new to Macaulay2, and I am trying to use it to help me with some linear algebraic computations over GF(8). How do I find the nullity (dimension of the kernel) of a matrix over GF(8)? Any help would be much appreciated.

Best,
Theo

[Federico Galetto]

Hi Theo,

You can compute the rank of your matrix with the "rank" function, and the number of columns with "numColumns".

By the rank-nullity theorem, the nullity can be computed as

numColumns(M)-rank(M)

if M is the name of your matrix. This should work over any field.

Cheers,

Fred.