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A note on commuting pairs of matrices. (English) Zbl 0754.15011
The paper contains: a short proof of the Motzkin-Taussky theorem on the irreducibility of the variety of commuting pairs of matrices, a consequence of this establishing that any two generated commutative subalgebra of $$n\times n$$ matrices has dimension at most $$n$$ and the proof of the result that the set of commuting triples of $$n\times n$$ matrices is not irreducible for $$n\geq 32$$.

##### MSC:
 15A27 Commutativity of matrices 15A30 Algebraic systems of matrices
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##### References:
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