Abstract
We have seen in Theorem 8.8 that the ortho-diagonalisable linear mappings on a complex inner product space are precisely those that are normal; and in Theorem 8.10 that the ortho-diagonalisable linear mappings on a real inner product space are precisely those that are self-adjoint. It is therefore natural to ask what can be said about normal linear mappings on a real inner product space; equivalently, we may ask about real square matrices that commute with their transposes. Our objective here is to obtain a canonical form for such a matrix under orthogonal similarity.
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© 2002 Springer-Verlag London Limited
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Blyth, T.S., Robertson, E.F. (2002). Real Normality. In: Further Linear Algebra. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-1-4471-0661-6_11
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DOI: https://doi.org/10.1007/978-1-4471-0661-6_11
Publisher Name: Springer, London
Print ISBN: 978-1-85233-425-3
Online ISBN: 978-1-4471-0661-6
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