Undergrad What does adjacent indices mean in the context of matrix multiplication?

[Oppie]

Hello, I was refreshing my Mathematics using S.M. Blinder's book "Guide to Essential Math" and on the section on Matrix Multiplication I got the following,

Can someone elaborate on the highlighted section? In particular, what does "adjacent indices" mean?

Thank you.

 

[andrewkirk]

'Elimination' just means that the result of the summation does not contain the index over which summation occurs. We see that from the fact that the RHS of the equation, which is just $y_i$, has no $k$ in it.

The word 'adjacent' is unnecessary in the sentence. Nor is the observation relevant only to matrices. For any summation, the summation index is annihilated in the result. Consider for instance:
$$\sum_{k=0}^nx^k=\frac{1-x^{n+1}}{1-x}$$
There is no $k$ on the right-hand side.

 

[Oppie]

'Elimination' just means that the result of the summation does not contain the index over which summation occurs. We see that from the fact that the RHS of the equation, which is just $y_i$, has no $k$ in it.

The word 'adjacent' is unnecessary in the sentence. Nor is the observation relevant only to matrices. For any summation, the summation index is annihilated in the result. Consider for instance:
$$\sum_{k=0}^nx^k=\frac{1-x^{n+1}}{1-x}$$
There is no $k$ on the right-hand side.

Thank you. Maybe he mentions the word "adjacent" in consideration to the summation convention.