I am looking for a quote of the following statement:
Vectors $v_1,v_2,...,v_n$ in a Hilbert space $H$ are linearly independent if and only if their gram matrix $G$ defined by $G_{ij}=\langle v_i,v_j \rangle$ is invertible.
I know this statement is true and I'd like to quote it in my thesis, however I did not find any book or paper that states this, and could only find the statement in the finite dimensional case.
Does anyone by any chance know a source that states this version? If not I suppose I could just prove it in the thesis, but since it's a pretty basic statement and not really interesting to the core of the thesis, a good quote would be the more elegant version.