meaning of subscript notation $\ 1_{a=a'}$

Question

I'm not familiar with the meaning of the 1 with the subscript notation $\ 1_{a=a'}$ and $\ 1_{b=b'}$, where (a,a') and (b,b') are simply coordinates of a matrix.

Could anyone explain this to me please?

Answer 1

I can't say for sure, since there isn't much context; but, frequently, the notation "$1_A$" (where $A$ is some statement) is used to represent the indicator function for that statement; that is, $$ 1_A=\begin{cases}1 & \text{if $A$ is true}\\0 & \text{if $A$ is false}\end{cases}. $$ So, in this case, I would suspect that $1_{a=a'}$ is meant to be $1$ if $a=a'$, and $0$ if $a\neq a'$.