Symmetrical matrices characteristic of integers with integer eigen value

• Main Author: PANDAPOTAN NAINGGOLAN (NIM : 90116006), SAHAT
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/30772
• Institution: Institut Teknologi Bandung

Estes (1992) stated that the set of eigen values 𝐸(𝑍) from symmetrical matrices of Z is a set of totally real algebraic integers. Estes was not able to ensure that eigen values of a symmetrical matrices 𝐴∈𝑀𝑛(𝑍) are integers. Mckee and Smyth (2007) observed more about the eigen value of symmetrical integer matrices. James and Chris proved that symmetrical integer matrices has eigen value with interval ranging in [−2,2]. Contrary to that, Martin and Wong (2009), stated that almost all integer matrices have no integer eigen value. Previous studies that could not show the characteristic of the eigen value made Cao and Koyunco studied and tried to determine the characteristic of symmetrical integer matrices for rank 2 and rank 3. The result shows that they have integer eigen value. In accordance to Cao and Kuyonco study, this article elaborates the characteristic of a symmetrical integer matrices for rank 4, 5 and even in a generalized rank, followed with programming algorithm, with maximum 10 x 10 matrices dimension, to show the characteristic of a symmetrical integer matrices with integer eigen value for rank 1, 2, 3, or even in a generalized rank.