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Complex eigenvalues; 4 matrices

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July 5, 2020
eigenvaluematriesMatriceslinear algebra

Problem Statement

Let be four n×n n\times n real matrices A,B,C,D A,B,C,D having the property that C+D−1 C+D\sqrt{-1} is the inverse of A+B−1. A+B\sqrt{-1} . Show that ∣det⁡(A+B−1)∣2⋅∣det⁡C∣=det⁡A. \left| \det\left( A+B\sqrt{-1} \right) \right|^2\cdot\left| \det C \right| =\det A.
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