MathDB

5

Part of 2022 VTRMC

Problems(1)

Eigenvalues of a Matrix

Source: VTRMC 2022 P5

1/4/2023
Let AA be an invertible n×nn \times n matrix with complex entries. Suppose that for each positive integer mm, there exists a positive integer kmk_m and an n×nn \times n invertible matrix BmB_m such that Akmm=BmABm−1A^{k_m m} = B_m A B_m ^{-1}. Show that all eigenvalues of AA are equal to 11.
VTRMCcollege contestslinear algebramatrixeigenvalue