Fast Fibonacci Jacket matrices transform

This paper presents the new notation called the Fibonacci Jacket matrices which can be algebraically constructed via Fibonacci numbers over Galois field GF(p). Based on the algebraic structure, such kind of matrices with some inverse-constrains belongs to Jacket matrices. Employing the well-known Kronecker product of sparse matrices and successively lower order Fibonacci Jacket matrices, the fast construction for large size Fibonacci Jacket matrices is described in detail. To decompose high order factorable Fibonacci Jacket matrices, a fast decomposition algorithm is suggested. Both the fast construction and decomposition transforms are presented for simplicity and clarity with the derived general recursive relations.