Talk:Linear dependence

Collinearity vs linear dependence

Collinearity is not the same as linear dependency. Say you put your row vectors in a matrix. The vectors are said to be collinear if the matrix is rank 1, and they are linearly dependent if the matrix is rank deficient (ie. has rank smaller than the number of vectors). This article actually seems to just be about linear (in)dependence, so just call it that.

- Sintel (talk) 22:54, 18 December 2021 (UTC)

Thanks for the critical feedback! This page is still potentially due for some revision as I iron out the final insights regarding it and temperament arithmetic. Okay. I see the difference in meaning. I came to this conclusion from interpreting a post I saw in the old Yahoo Groups thread archives. Perhaps in xenharmonics the usage of the word got stretched a bit. So would you say my section on this page "Vs geometry" is just totally inaccurate? If so, I can delete it.

My remaining concern, then, is that I needed a word to describe a condition on the possibility of temperament arithmetic. And I called it, for now, "monononcollinearity", and it builds upon the notion of collinearity that is described here, i.e. linear dependence. So I should replace that term, I suppose, with "singularly linearly independent", meaning when two temperaments share all but one vector. The problem is that I need to use that word *A LOT*, and "singularly linearly independent" is a mouthful. Do you happen to know if there's already an established term for this? I tried searching online for it but met no success. If you entry-wise add multivectors that are not singularly linearly independent, you get a multivector that is nondecomposable, i.e. cannot be expressed as the wedge product of vectors. --Cmloegcmluin (talk) 03:16, 19 December 2021 (UTC)