5 comments on “Tensor Algebra

  1. Jide says:

    Thanks

  2. Anih John says:

    Good evening sir,

    Just to remind you. You said, you were to going to give us a PDF to enable us do the homework i.e Gurtin 2.6.1, 2.8.5 etc…

    Thank you sir.

  3. Abdul-Hammid says:

    Homework 2.1 (Question 4)
    To show that Tu,Tv and Tw are linearly independent, the scaler triple product must not be zero.

    [Tu,Tv,Tw] = Tu.(Tv x Tw) =
    expressing the vectors u,v and w in its component form…
    Tuiei.(Tvjej x Twkek) = eijkuivjwk(Tei.(Tej x Tek))…
    How do I continue from there sir???

    • oafak says:

      If T is not singular, if Tu,Tv and Tw are also linearly dependent, then ∃α,β and γ all real such that αTu+βTv+γTw=o. But u,v and w are linearly independent. This means that αu+βv+γw≠o.
      αTu+βTv+γTw= T(αu+βv+γw)=o.
      This means that αu+βv+γw=o. This states that set of linearly independent vectors is linearly dependent! That is a contradiction!

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