Ciro Santilli @cirosantilli 40

When we have a symmetric matrix, a change of basis keeps symmetry iff it is done by an orthogonal matrix, in which case:

The change of basis matrix $C$ is the matrix that allows us to express the new basis in an old basis:

Mnemonic is as follows: consider we have an initial basis $(x_{old},y_{old})$. Now, we define the new basis in terms of the old basis, e.g.:which can be written in matrix form as:and so if we set:we have:

The usual question then is: given a vector in the new basis, how do we represent it in the old basis?

The answer is that we simply have to calculate the matrix inverse of $M$:

That $M^{-1}$ is the matrix inverse.

See: Video "Your Life is Your life by Charles Bukowski".

Basically it looks like the dude got enough money after selling some companies, and now he's doing cooler stuff without much need of money. Not bad.

TODO instance of what?

Chemistry is fun. Too hard for precise physics (pre quantum computing, see also quantum chemistry), but not too hard for some maths like social sciences.

And it underpins biology.