Jacket matrix

In mathematics, a Jacket matrix is a square matrix A=(a_{ij}) of order n whose entries are from a field ( including real field, complex field, finite field ), if

$AA^{\mathrm {*} }=A^{\mathrm {*} }A=nI_{n}$

where A^{\mathrm{*}} is the transpose of the matrix of inverse entries of A , i.e. A^{\mathrm{*}}=(a_{ij}^{-1}).

References

 M.H. Lee, The Center Weighted Hadamard Transform, IEEE Trans.1989 AS-36, (9), pp.1247-1249.  M.H. Lee, A New Reverse Jacket Transform and its Fast Algorithm, IEEE Trans. Circuits Syst.-II , vol 47, pp.39-46, 2000.  M.H. Lee and B.S. Rajan, A Generalized Reverse Jacket Transform, IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process., vol. 48 no.7 pp 684-691, 2001.  J. Hou, M.H. Lee and J.Y. Park, New Polynomial Construction of Jacket Transform, IEEE Trans. Fundamentals, vol. E86-A no. 3, pp.652-659, 2003.  W.P. Ma and M. H. Lee, Fast reverse Jacket Transform Algorithms, Electronics Letter, vol. 39 no. 18 , 2003.