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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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