Conjugate transpose

Conjugate transpose is a special kind of math calculation. To understand what it does, imagine that you have two sets of numbers, like two friends who are each keeping track of the number of toys they have collected. The first friend might write down "2, 4, 8" which means that he has 2, 4 and 8 toys in total. The second friend might write down "5, 9, 3" which means that he has 5, 9 and 3 toys.

If you want to know how many of the same toys they have in total, you can do a conjugate transpose. To do this, first you take the numbers the first friend wrote down and reverse them. So, "2, 4, 8" would become "8, 4, 2". Then, you multiply each number in the reversed set by the corresponding number from the second set. So, "8, 4, 2" times "5, 9, 3" would be 8*5, 4*9, and 2*3 which comes out to 40, 36, and 6. Adding those up, you get 42 which tells you that both friends have a total of 42 toys.