This might be of some help.
represents element of the matrix.
represents row of the matrix
represents column of the matrix
it is in place of
How are these different?
My book proves the distributive property of multiplication as follows (im going to leave stuff out)
Then you expand AB+AC and do some regrouping to find A(B+C)=AB+AC
But, in another text I found the same proof done with the afore mentioned notation
I don't understand how to read the latter proof. What's being done in the proof makes sense to me, but I'm just not sure how to read the notation I guess.
Essentially they are the same with , and as malaygeol sort of said, .
Also, is the entire matrix while is just one element of it, and also (I presume) the such that is different from the such that , if that makes sense...
With notation problems like this I tend to just guess - if you understand what it is mean to be then you can often work out what the notation means. If it makes sense it is probably true.