Vol. 43, No. 2, 1972

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Algebras of normal matrices

George Maxwell

Vol. 43 (1972), No. 2, 421–428

A classical theorem of matrix theory asserts that a commuting set of complex normal matrices can be simultaneously unitarily diagonalised. In this paper, this result is generalised, both for the field of complex numbers and for more general fields. Namely, a commuting set of normal matrices is replaced by a subalgebra composed entirely of normal matrices. The structure of such subalgebras is determined and results on simultaneous diagonalisation are deduced. In the complex case, these subalgebras turn out to be commutative. However, even in the real case there are noncommutative examples.

Mathematical Subject Classification 2000
Primary: 15A30
Secondary: 16A40
Received: 17 June 1971
Revised: 6 June 1972
Published: 1 November 1972
George Maxwell