Suppose we have a symmetric matrix $M\in\operatorname{Sym}{M}_{n}(\mathbb{Z})$ having some negative eigenvalues. Are there algorithms filling the entries of a (possibly) bigger symmetric matrix $M'\in\operatorname{Sym}{M}_{m}(\mathbb{Z})$ whose entries $M'_{i,j}$ are obtained with the same formula for all cases (that is, uniformly for any example) as integer (that is, with coefficients in $\mathbb{Z}$) linear combinations of the entries in the original matrix $M$ such that the eigenvalues of this new and possibly bigger symmetric matrix $M'$ are all positive (that is, the matrix is positive definite) and $\det(M)$ divides $\det(M')$?
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