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Math Help - Tranposed Matrix Product

  1. #1
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    Tranposed Matrix Product

    The product of two transposes satisfies
    (2)
    (3)
    (4)
    (5)
    (6)

    where Einstein summation has been used to implicitly sum over repeated indices.


    I don't understand this proof. From (3) to (4) they are using the commutative property on the product of two matrices? I thought that wasn't true in general.
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  2. #2
    Member alunw's Avatar
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    No they are using the commutativity of multiplication in the underlying number field that the matrices are using.
    But your point is good since it means you would have to be careful if you wanted to manipulate matrices over a skew field. Then this result would not be true, and probably some other usual results about matrices would not be true either.
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