I am very naive when it comes to advanced mathematics, so consider me a layman. I am currently taking a course in Quantum mechanics and I've been introduced to the concept of functions being infinite dimensional vectors.
We however covered only functions of one variable and the math makes sense to me (the dot product, projecting functions onto the x basis etc. )
But how do these properties generalize to more than variable? What would be the dot product? I guess a double integral.
So, it would be very helpful if someone can generalize concepts in layman's terms or link some web pages that explain this as I couldn't find any.