How does one write the following expression D_(jk)(r_k delta_(ij)−r_i delta_(jk)−r_j delta_(ik)) in matrix notation? Is this just bb(D(r xx I))?

pulpenoe 2022-09-25 Answered
How does one write the following expression
D j k ( r k δ i j r i δ j k r j δ i k )
in matrix notation? Is this just
D ( r × I )?
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Answers (1)

Edward Chase
Answered 2022-09-26 Author has 10 answers
The given expression in matrix notation should be:
( D D'   trace ( D ) ) r
By applying the Kronecker Delta we have:
D j k ( r k δ i j r i δ j k r j δ i k ) = D j k r k δ i j D j k r i δ j k D j k r j δ i k = D i k r k D k k r i D j i r j
I was not able to find a cross product (Levi-Civita expression) from the given Kronecker Detla Expression.
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