MathDB

6

Part of 2017 Korea USCM

Problems(1)

matrix relation, every entry 1 matrix

Source: 2017 South Korea USCM P6

8/15/2020
Given a positive integer nn and a real valued n×nn\times n matrix AA. JJ is n×nn\times n matrix with every entry 11. Suppose AA satisfies the following relations. A+A^T = \frac{1}{n} J,   AJ = \frac{1}{2} J Show that Am−IA^m-I is an invertible matrix for all positive odd integer mm.
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