Characteristics of special matrices which is defined by integer sequences with different step

In this work we are considered the norm of matrices as Euclidean norm, spektral norm, 1-norm and infinity norm which is defined by Lucas and companion-Lucas sequences with second step integer sequences. After that eigenvalues and determinants are found for these matrices. Same results are obtained for tetranacci and companion-tetranacci integer sequences so these results have been expanded to the fourth step. Finally, the family of tridiagonal matrix are investigated which is connected parameter k related to be defined k-balancing numbers.