Generalized Method to Find the Generators of Matrix Algebras when its Dimension 2 and 3
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Keywords:Generator, Matrix, Common left eigen vector, Sub Algebra
Let A be an algebraically closed field of characteristic zero and consider a set of $2 \times 2$ or $3 \times 3$ matrices. Using a theorem of Shemesh, we give conditions for when the matrices in the set generate the full matrix algebra.
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