Contraction

40 In a contraction, we make two of the indeces equal (or in a mixed tensor, we make a ubscript equal to the superscript), thus producing a tensor of order two less than that to which it is applied. For example:

-J-tJ

ii

2 —

G

UiVj -

UiVi;

2 —

G

. .sn

Amr A..sm

= Brs;

4 —

2

Eij ak -

-> Eij ai

= cj ;

3 —

Aqs

Ampr Aqr

= Bq™p;

5 —

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