CODEWITHSUNDEEP
matlablinear-algebra
matlab-oh-no
matlab-oh-no

Reputation: 51

Reduced row echelon matrix equivalence

I've been trying to solve whether two m-by-n matrices A and B are equivalent via

[a,ja] = rref(A,tol)
[b,jb] = rref(B,tol)

and then comparing

isequal(a,b) & isequal(ja,jb)

First, I don't really understand what ja and jb are. My problem is that the reduced row echelon form is very simple for both A and B and identical in all cases. I don't know whether this is on purpose or not. For example, I get equivalence for just

A = rand(40,3)
B = rand(40,3)

which I'm not sure is nonsense or not.

Upvotes: 0

Views: 820

Answers (1)

horchler
horchler

Reputation: 18484

It looks like you're trying to check if the reduced row echelon forms of two matrices are element-wise equivalent. From how you've defined A and B, they are (it's effectively an overdetermined system, I believe). However, I think that you may have flipped your rows and columns. If instead you create A and B such that there are more columns than rows (i.e., an augmented matrix of an underdetermined system):

A = rand(3,40)
B = rand(3,40)

then when you run rref, you'll see a much different output and your comparison will return false as you perhaps expected.

Also, I think that it is sufficient to use the following, as two matrices that are equal element-wise will surely share the same rank (or approximation thereof):

a = rref(A,tol);
b = rref(B,tol);
isequal(a,b)

Upvotes: 1

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