For any $nxn$ positive definite symmetric matrix $A$ is it possible to write it's entries $a_{ij}$ as inner products of vectors $v_1,v_2,....,v_n$, that is $a_{ij}=\langle v_i,v_j\rangle$? Is there a deterministic way to find $v_1,v_2,....,v_n$ for any given $A$? I thought maybe Cholesky decomposition would be the best way to do it. Have I missed something? Is there any easier way?
Thanks!