Is Your Vector Infinite Dimensional?

The reason why a wave on is like an infinite dimensional vector, and these operators that are observing properties about the object that we're trying to describe are infinite dimensional matrices. Position is a continuous spectrum. And so if you want to describe your state and the position representation, you need be able to tell me the probability amplitude to find your thing at this position, for every single position. That's why your vector's infinite dimensional,. just infinite and infinite amount of frent positions that you can find the amplitude for. When operating on it, you're basically just doing matrix multiplication.