Linear Operators on Hyperbola and Hyperboloid

Jacket matrices which are defined to be mtimesm matrices J = [j
_ik
] over a field F with the property JJ
^dagger
= mI
_m
, J is the transpose matrix of elements inverse of J. i.e., J
^dagger
= [j
_ik

^-1
]
^T
, was introduced by Lee in 1984 and are used for digital signal processing and coding theory. This paper presents some square matrices A
_2n
which can be eigenvalue decomposed by Jacket matrices. Specially, A
₂
and its extension A
₃
can be used for modifying the properties of hyperbola and hyperboloid, respectively. The ideas that we will develop here have applications in computer graphics and used in many important numerical algorithms.