- Equation (3.54) can be thought of as an
equation in an
dimensional vector space
with a linear operator
**F**acting on a vector function**a**(*t*) on the right hand side, and a differential operator acting on**a**(*t*) on the left hand side. There is a standard way to solve such equations. The way is as follows:- If
**F**is a*normal*operator, i.e., then it is possible to find such*rotation*in , i.e., such transformation that when we rotate the basis of the vector space, the operator**F**in the new basis will be diagonal. - If
**F**is not*normal*then a diagonalizing transformation still exists, but it may not be in . This is not a big problem: things just get a little more messy. - Once
**F**has been diagonalized equation (3.54) splits into*n**independent*differential equations that can be solved trivially. - Then we have to rotate things back to the original basis.

- If

- Rotating the Basis of the Vector Space
- The Eigensolution and its Transformation
- A Comment about the Lambdas