A note on Eigenvlaue decomposition on Jacket transform

Jacket transforms are defined to be n x n matrices A = (alpha_jk) over a field F with the property AA⁺ = nl_n, where A⁺ is the transpose matrix of elements inverse of A, i.e., A+ = (alpha_kj ^-1 ), which generalized Hadamard transforms and center weighted Hadamard transforms. It has been found that the Jacket transforms are applied to signal and image representation and compression. This paper propose a new eigenvalue decomposition method with Jacket transform. The eigenvalue decomposition methods discussed here may be applied to doubly stochastic processing and the information-theoretic analysis of multiple input multiple output (MIMO) channels.