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I was sure we already had a thread about math, but I can't find it in the catalogue. So here is a new one.

And I'll just start it off with a question that I have trouble finding a conclusive answer to:

In a vector space the subspace spanned by the rows is perpendicular to the kernel, it is also orthogonal to it; is there a difference between perpendicularity and orthogonality of subspaces?

This relates to: If I have brought a matrix into rref with Gauss-Jordan, I can simply read a basis for the column space from the first r pivot columns (r being the rank of the matrix) and I'm wondering if I can read something about the basis of the kernel from the remaining columns (or rows?).

And I'll just start it off with a question that I have trouble finding a conclusive answer to:

In a vector space the subspace spanned by the rows is perpendicular to the kernel, it is also orthogonal to it; is there a difference between perpendicularity and orthogonality of subspaces?

This relates to: If I have brought a matrix into rref with Gauss-Jordan, I can simply read a basis for the column space from the first r pivot columns (r being the rank of the matrix) and I'm wondering if I can read something about the basis of the kernel from the remaining columns (or rows?).