Hilbert space vs vector space in simple words

#hilbertspace #hilbertspacevsvectorspace #sayphysics
0:00 difference between Hilbert space and vector space
0:37 what is vector spaces
2:14 what are bases of a vector space
4:46 linear combinations in a vector space explained
7:00 Hilbert space in quantum mechanics
15:55 Fourier trick and Hilbert space

Lecture Notes: https://drive.google.com/open?id=1HcK...
Difference between Hilbert space and Vector space
What is Hilbert space
An Introduction to Hilbert Spaces
First let's talk about the vector space, it is a three-dimensional space, the 𝑥𝑥, 𝑦𝑦 and 𝑧𝑧 we call the unit vectors. What are their properties? The properties are if you take the magnitude of these, which will be equal to 1. If you need the dot product of each of them with each other then they will be equal to 0. Why? Because they are perpendicular to each other. This condition shows orthogonally and can mean that these unit vectors are normalized. The unit vectors are orthonormal in nature.