# Resolution of the Identity

1. Oct 8, 2011

### franklampard8

How do I prove that

Ʃ\ket{ei} \bra{ei} = I

2. Oct 8, 2011

### strangerep

It depends on the context, and precisely what your $e_i$ stand for.

As a general suggestion, start by looking up the "spectral theorem" in a linear algebra textbook. (Wikipedia gives an overview, though not the details.)

3. Oct 8, 2011

### franklampard8

$e_i$ refers to a finite orthonormal basis

4. Oct 8, 2011

### strangerep

OK, so if you write out how an arbitrary vector $\psi$ is expressed in terms of that orthonormal basis, the desired answer should then follow almost immediately.