Hilbert space vs vector space in simple words

Buy this complete course on Udemy https://www.udemy.com/course/quantum-mechanics-i/?referralCode=7BCA66A4AA2BE98FC178 #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=1HcKcDvbVN_M4yCJ27b5YOos6gyLm5YEJ 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.