A second-order Hadamard matrix may be defined by
with higher order Hadamard matrices defined by recursive embedding, e.g.,
When is a power of , the Hadamard matrix of that order requires no multiplies in fixed-point arithmetic. An Hadamard matrix has the maximum possible determinant of any complex matrix containing elements which are bounded by in magnitude. This can be seen as an optimal mixing and scattering property of the matrix.
As of version 0.9.30, Faust's math.lib4.12contains a function called hadamard(n) for generating an Hadamard matrix, where must be a power of . A Hadamard feedback matrix is used in the programming example reverb_designer.dsp (a configurable FDN reverberator) distributed with Faust.
A Hadamard feedback matrix is said to be used in the IRCAM Spatialisateur .