Ciro Santilli @cirosantilli  40

Ciro Santilli had to see this in a few separate places, until he underestood: that little pictur emust be a thing! Examples:

In this section we list charitable organizations that support education or research:

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.

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

Examples:

Power, Sex, Suicide by Nick Lane (2006) part 5 "Murder or suicide" mentions that apoptosis has two main functions: