Given that $R$ is a rectangular matrix, $D$ is a diagonal, square matrix and $S$ being a square matrix along with the fact that both $D$ and $S$ are invertible. $S$ in this specific case can be assumed to be symmetric, positive-definite.$R$ is actually the first few columns of the discrete Fourier Transform matrix. Thus, $R^{T}R=Id $. Note $RR^{T}$ need not be $Id$. Also, $R$ has both dimensions of the same order (but with more rows than columns). $R$ also has a full row rank.I would like to obtain $D$ in terms of the given matrices, which are $R$ and $S$
Solve for $D$ in $R^{T}DSDR = Id$
linear solver;matrix