Question

How can I turn a regular matrix into a matrix full-ranked in R? Is there an available method for that?

I have a matrix that may have linearly dependent columns and I need to
pass it to a function that requires its argument to be a matrix with
full rank. Since linearly dependent columns are not of interest
anyway, I am looking for a function that removes such columns until
the matrix is full rank. There may be several solutions of course, but
any one of them should be fine.

Right now I am just constructing the matrix column by column and only
add a column if its the resulting matrix is still fullrank, but it
feels like there should be a better way to do this.

Answer 1

Another approach is to minimize |y – Ax|² + c |x|²,
by tacking an identity matrix on to A and zeros to y.
The parameter c (a.k.a. λ)
trades off fitting y – Ax, and keeping |x| small.
Then run a second fit with the r largest components of x,
r = rank(A) (or any number you please).