Journal of University of Duhok, Vol. 21, No.1 (Pure and Eng. Sciences), Pp 1-5, 2028 DOI: https://doi.org/10.26682/sjuod.2018.21.1.1 * E-mail: honer.naif@uod.ac 1 USING FIBONACCI NUMBER TO INTEGRATE  AND  MATRICES HONER N. ABDULLAH * , DELBRIN H. AHMED and MUWAFAQ M. SALIH Dept. of Mathematics, College of Basic Education, University of Duhok, Kurdistan Region-Iraq (Received: June 13, 2017; Accepted for Publication: April 30, 2018) ABSTRACT The aim of this paper is to make the clarification of images faster by the formula that Franciszekn made for matrices integrations and this made Sukhvinder’s Algarithm complicate and slower. Tis paper uses Fibonacci number to determine integration formulas for matrices of order 2 and 3 in order to make the process of images clarification shorter. 1. INTRODUCTION he Fibonacci numbers (Fibonacci sequence) were invented by Italian Leonardo Pisano Bigollo in his book called’’Liber Abaci’’. Furthermore, the integration of matrices is used to avoid image ambiguous. Franciszekn[1] used anti-orthogonality of matrix to find its integration, but that formula made the Sukhvinder’s[7] algorithm complicate and the process became slow where the orthogonality founded interest in the [4],[7],[6]. Penner[3]use double integral to find the matrix integration. While Rnadal [4] found the derivative of the matrix for some special cases. In this paper, we used Fibonacci number formula to find the formula of integration of matrix in diminution 2 and 3. 2. SOME DEFINITIONS AND MATRIX DERIVATIVE In this section, we see the basic definition that are going to be used in section two moreover some proposition of how to derivative matrix. Definition of Matrix 2.1[4] The order rectangular              where    then                           is said to be matrix of  dimension. Definition of First Order Partial Derivative 2.2[4] Let    where  is vector with  element and  is  element vector so                                   The matrix we get is  of first order partial derivative. Definition 2.3[3] The Fibonacci number  are defined by the equation       where      and . T