A Symmetric Eigenvalue Decomposition Example in under Three Minutes!

[danielellis]

I wish there were more videos like this out there. There's so much packed into this one simple example. It makes it really easy to pause and understand each concept before moving on. I've read about orthonormal vectors, orthogonal vectors, etc a ton of times, but it never fully stuck. It's really easy to see how they relate to the broader picture now that I see all of the concepts connected to something specific.

[anekleynhans]

Im so sorry this is a silly question, but where does the 1 1 come from

[sachinmotwani]

Shouldn't it have an inverse on the top of the last matrix? (According to the EVD notation)

[SuperYtc]

Why are the eigenvectors normalised but the eigenvalues aren't?

[Hythloday]

I've recently come to a philosophical position / belief. This is, no true item of reality can be 'cancelled' out. A corollary is no 'true' item of reality is in essence a 'composition'' of other items of reality. It is an open question whether we can ever probe 'items of reality' but the apparent naive presentation would support this 'starting' premise in my version of realism.
I contend that all vector space phenomena 'in reality' are then emergent, as waves in the sea can be viewed as sloshing loosely bound particles, or waves in string or elastic as tightly bound bound particles with coupling co-efficients of coupled oscillators.
I thought I'd run this by you. I don't believe in Fields as fundamental because it hypothesises variable numbers in space without mechanism. Vector spaces & fields thus are just a useful tool to physics and an interesting structure to the mathematician.