Jacket Matrix in Hyperbola

Jacket matrices[2][8] which are defined to be m ×m matrices † 1 Tik J = ??J− ?? over a Galois field F with theproperty †m JJ =mI , J † is the transpose matrix of element-wise inverse of J , i.e., † 1 Tik J = ??J− ?? , were introducedby Lee in 1984 and are used for Digital Signal Processing and Coding theory. This paper presents some squarematrices 2 n A which can be eigenvalue decomposed by Jacket matrices. Specially, 2 A and its extension 3 A canbe used for modifying the properties of hyperbola and hyperboloid, respectively. Specially, when the hyperbola has times transformation, the final matrices 2A n can be easily calculated by employing the EVD[7] of matrices2 A . The ideas that we will develop here have applications in computer graphics and used in many importantnumerical algorithms.