Abstract
In a previous paper we characterized unilevel block α -circulants A = [ A s - α r ] r , s = 0 n - 1 , A m ∈ C d 1 × d 2 , 0 ⩽ m ⩽ n - 1 , in terms of the discrete Fourier transform F A = { F 0 , F 1 , … , F n - 1 } of A = { A 0 , A 1 … , A n - 1 } , defined by F ℓ = 1 n ∑ m = 0 n - 1 e - 2 π i ℓ m / n A m . We showed that most theoretical and computational problems concerning A can be conveniently studied in terms of corresponding problems concerning the Fourier coefficients F 0 , F 1 , … , F n - 1 individually. In this paper we show that analogous results hold for ( k + 1 ) -level matrices, where the first k levels have block circulant structure and the entries at the ( k + 1 ) -st level are unstructured rectangular matrices.
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