Hey, I have a question.

I was thinking about linear indepence of columns of matrices etc. and how they are all connected with eigendecomposition, i.e. number of nonzero eigenvalues is also the rank of the matrix.

So here is the question. Lets say i defined a new "dependence" called "scalar dependence", where I determine if a column (or row doesnt matter) is a scalar multiple of another. If it is not scalar multiple, I say determine that column is "scalarly independent" of others. Is there such a definition somewhere in linear algebra? How would eigen decomposition change in such a case?