@article{article_431628, title={On The Properties Of The Complex Fibonacci And Lucas Numbers With Rational Subscript Via Roots Of The Fibonacci Matrix}, journal={Erzincan University Journal of Science and Technology}, volume={12}, pages={148–157}, year={2019}, DOI={10.18185/erzifbed.431628}, author={Köken, Fikri}, keywords={Fibonacci dizileri,Matris fonksiyonları,Kök matrisleri}, abstract={<p> <span lang="en-us" style="font-size:12pt;line-height:18.399999618530273px;font-family:’Times New Roman’, serif;" xml:lang="en-us">In this study, we exploit general techniques from matrix theory to establish some identities for the complex Fibonacci and Lucas numbers with rational subscripts of the forms  <span> </span> and  <span> </span>. For this purpose, we establish matrix functions  <span> </span> and  <span> </span> of the Fibonacci matrix  <span> </span> of order  <span> </span> for integer odd  <i>n </i>and discuss some relations between two special matrices functions  <span> </span> and  <span> </span>, respectively. Also, some identities related to the complex Fibonacci and Lucas numbers with rational subscripts of the forms  <span> </span> and  <span> </span> are given for every integer odd  <i>n  </i>and <span> </span>, respectively. </span> <span style="font-family:’-webkit-standard’;font-size:medium;"> </span> <br /> </p>}, number={1}, publisher={Erzincan Binali Yildirim University}