Conference Proceedings of Science and Technology, cilt.3, ss.102-109, 2020 (Düzenli olarak gerçekleştirilen hakemli kongrenin bildiri kitabı)
The Fibonacci number sequence and related calculations come up in scientific facts in many events that we encounterin daily life. This special number sequence is processed in the occurrence of many events such as calculating the diameter ofthe equatorial circumference of the Earth, flowers, growth and structures of leaves, trees, reproduction of bees, sunflower andso on . However, in recent years, the relation between the Fibonacci and Lucas Number sequences with continued fractionsand matrices has intensively been studied. Many identities have been found by some2×2types of special matrices with thenthpower that have been associated with the Fibonacci and Lucas numbers. The aim of this study is to examine matrix(1 1−1 0)under the Lorentzian matrix product with thenthpower, quadratic equations and characteristic roots unlike the classical matrixproduct. In addition, we want to acquire some identities with the help of matrix(1 1−1 0)under the Lorentzian matrix productwith thenthpower in relation to the Fibonacci and Lucas numbers.