Generalisation
The above equations can be expressed in matrix algebra, by considering a and b as two elements of a vector, and the transform itself as multiplication by a matrix of the form:
The inverse can then be derived by inverting the matrix.
However, the matrix can be generalised to higher dimensions, allowing vectors of any power-of-two size to be transformed, using the following recursive rule:
For example:
Read more about this topic: Pseudo-Hadamard Transform