Hilbert Spaces 1 | Introductions and Cauchy-Schwarz Inequality

[@lukephillips7239]

Im trying to teach myself wuantum mechanics and this tipic is quite relevant.

[@brightsideofmaths]

Indeed! For quantum mechanics you need a good knowledge of Hilbert spaces and operators on them.

[@sonicmaths8285]

Hello Bewwy Cwipke

[@kyteris0624]

Professor, when you introduce the definition of inner product around 5:45, I wondered why you wrote it as a linear with respect to second component. By the definition of the inner product, it is a linear with respect to the first component. For the second component, if the field is a real number, this is not a problem, but if the field is a complex number, it will be conjugate.

[@brightsideofmaths]

There are two conventions around how to define the inner product. I chose this one because it has advantages in remembering some formulas.

[@teddy05p]

Amazing:) please keep it up, im doing this course right now, interested to see your teaching in comparison to my professors :)

[@brightsideofmaths]

Thanks :)

[@itscristianodasilva]

This video came at the perfect time, I have this on my linear algebra midterm

[@ni2371]

Hey, first I (hopefully a future physicist) want to say I really love and admire your work! Thank you. Secondly, I'm really curious how you managed to upload videos of the same topics but with a dark background without recording them from scratch.

[@brightsideofmaths]

Thanks a lot. And thanks for the support. The dark version is just colour swapping.

[@ybc8495]

@@brightsideofmaths color of conjugate.