We may define the **components of a state vector**
as the projections of the
state on a complete, orthonormal set of states, like the eigenfunctions of a Hermitian operator.

Similarly, we may define the

With these definitions, Quantum Mechanics problems can be solved using the
matrix representation operators and states.
An operator acting on a state is a matrix times a vector.

The product of operators is the product of matrices. Operators which don't commute are represented by matrices that don't commute.

Jim Branson 2013-04-22