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- Does performing an elementary column (or row) operations count as a change of basis? Perhaps this is merely a vocabulary question about how people use the phrase "change of basis".

A blog post by Evan Chen https://blog.evanchen.cc/2016/07/12/the-structure-theorem-over-pids/ says that elementary row and column operations on a matrix can be interpreted as a change-of-basis.

I assume this use of the phrase "change of-basis" refers to creating a matrix that uses a different basis for a vector in its domain (as a linear tranformation) than in its range. Is that correct?

I assume this use of the phrase "change of-basis" refers to creating a matrix that uses a different basis for a vector in its domain (as a linear tranformation) than in its range. Is that correct?