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貓朋
Lv 5
貓朋 發問於 科學及數學數學 · 1 十年前

Relation between Alternator and Kronecker delta (Matrix)

This question is extracted from the Exercise 1.3 of Continuum Mechanics: Concise Theory and Problems

Please be reminded that, under the summation convention, δij =3

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  • Ivan
    Lv 5
    1 十年前
    最愛解答

    Remind you that, in the exercise, summation convention is NOT used!

    Fix i,j,k,l,m,n,.

    take Ai1 = 1, Aj2 = 1, Ak3 = 1, and all the other entries 0

    take Bl1 = 1, Bm2, = 1, Bn3 = 1, and all the other entries 0

    i.e. The column of A is [δip, δjp, δkp], column of B is [δlp, δmp, δnp] (p = index of column entries)

    Then detA detB gives you the left hand side

    det A' B, using the usual calculation of determinant of 3x3 matrix, will give you the right hand side, where the entries is given by multiplication of δ, with summation index. for example, the first entry is δip . δlp = δil

    資料來源: PhD Math
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