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Finding centraliser algebras of a finite set of matrices

Let $S$ be a finite set of $n \times n$ -matrices over a field $K$ (lets say finite or the real or complex field).

Is it possible to obtain the $K$ -algebra (or at least its vector space dimension) of $n \times n$ -matrices X in Sage with $XY=YX$ for all $Y \in S$ ?

Finding centraliser algebras of a finite set of matrices

Let $S$ be a finite set of $n \times n$ -matrices over a field $K$ (lets say finite or the real or complex field).

Is it possible to obtain the $K$ -algebra (or at least its vector space dimension) of $n \times n$ -matrices X in Sage with $XY=YX$ for all $Y \in S$ ?

(I can only think of a way for doing this for finite field with very small $n$ by looking at all elements,but maybe there is a better technique in Sage)