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How to efficiently calculate the inverse of the overlap matrix?

Now, we consider a non-orthonormal basis: $$\mathcal{S}_N=\{|\alpha\rangle,a^\dagger|\alpha\rangle,a^{\dagger 2}|\alpha\rangle,\ldots,a^{\dagger N}|\alpha\rangle\},$$ where $|\alpha\rangle$ is the ...
Young Q's user avatar
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Are there ways to find representations of matrices given an algebra?

Given an equation (or a set of equations) involving matrices, is there an algorithm to find possible representations of these matrices? For example, we can consider a matrix $A$ such that $A^2=\begin{...
YeetTheorem's user avatar