AngelofMusic
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Hi,
We recently started analyzing linear machines using matrix algebra. Unfortunately, I haven't had much exposure to operating in finite fields aside from the extreme basics (i.e. the definitions of GF(P)). I can get matrix multiplication/addition, etc. just fine, but it's when finding the properties of a matrix that I'm confused.
How do we know if the rows of a matrix over GF(p) are linearly independent?
More specifically, how can I tell if two nonidentical matrices have the same row space, or if the row space of matrix A is a subspace of the row space of matrix B?
I suspect the answer to my first question is just to do Gaussian elimination and look at the rank instead of doing any algebraic manipulation such as (c1*row1 + c2*row2... ) and so forth.
But suppose I've got two matrices in row echelon form. How would I compare the rowspans of both matrices once I've done that?
I may be missing something very obvious, so your patience is appreciated!
We recently started analyzing linear machines using matrix algebra. Unfortunately, I haven't had much exposure to operating in finite fields aside from the extreme basics (i.e. the definitions of GF(P)). I can get matrix multiplication/addition, etc. just fine, but it's when finding the properties of a matrix that I'm confused.
How do we know if the rows of a matrix over GF(p) are linearly independent?
More specifically, how can I tell if two nonidentical matrices have the same row space, or if the row space of matrix A is a subspace of the row space of matrix B?
I suspect the answer to my first question is just to do Gaussian elimination and look at the rank instead of doing any algebraic manipulation such as (c1*row1 + c2*row2... ) and so forth.
But suppose I've got two matrices in row echelon form. How would I compare the rowspans of both matrices once I've done that?
I may be missing something very obvious, so your patience is appreciated!