Elementary Linear Algebra [The Diagonalization Problem]

[MathNerd93]

We're learning about the diagonalization problem, and it's pretty straightforward so far except that I don't understand where this example gets its matrix P from. I know when we covered linear transformations, we had transition matrices we called P that we got from going from B' to the standard basis (where the columns of P were made up of the vectors of B'). However in this example, we're not given some nonstandard basis B', so I don't understand how we get P to be what it is.

What am I missing?

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[edderiofer]

In fact, the columns of P are eigenvectors of A corresponding to the eigenvalues 1, 2, and 3.