- #1

- 39

- 0

(a x b) = ε

_{ijk}a

_{j}b

_{k}

ε

_{ijk}ε

_{iab}= δ

_{ja}δ

_{kb}δ

_{jb}δ

_{ka}

δ

_{ij}a

_{j}= a

_{i}

## Homework Statement

Here's the problem I'm trying to solve: Which of the following are allowed in index notation:

a = b

_{i}c

_{ij}d

_{j}

a = b

_{i}c

_{i}+ d

_{j}

a

_{i}= δ

_{ij}b

_{i}+ c

_{i}

a

_{k}= b

_{i}c

_{ki}

There are a whole bunch more of these, but I think I can probably figure those out if I get some help with these. Please explain which of those are allowed in index notation and why they are allowed or not allowed. Thanks!

## Homework Equations

## The Attempt at a Solution

I'd say that the first is allowed because neither i nor j is repeated more than twice.

Same with the second.

For the third, I know δ

_{ij}b

_{i}= b

_{j}but then I'm not sure what to make of it from there.

The fourth seems okay since k is the free variable and we're summing over i.

Thanks again for your explanations!