its like this...

a toffoli gate does the operation

|00> to |00>

|01> to |01>

|10> to |11>

|11> to |10>

so the elements of the matrix belonging to the ; ; ; will be 1 and rest will be zero!

thats all what is represented in the matrix.

the ij elements of the matrix are the ket and the bra state,,,,

hope i helped....

Thank you for the reply

so I am now guessing the reason I do not understand the matrix notation is that it is more related to quantum computers

I can understand the basic working of the Toffoli gate as explained in Wikipedia (it seems to be a basic type of combinational logic circuit) but I do not understand the bra-ket notation nor the matrix one

i will suggest u to read a book... "Quantum computing explained" by David McMahon... its a very basic book for Quantum Computing and also Dirac (i.e. Bra-Ket) notations... it will help!! :)

Unfortunately, it's not available to me right now

However I have a book called "Principles of quantum communications volume 1" by Beneti, Casati and Strini

Would it be ok for a complete beginner?