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Beyond Eigenspaces: Real Invariant Planes

Linear Algebra: In the context of real vector spaces, one often needs to work with complex eigenvalues. Let A be a real nxn matrix A. We show that, in R^n, there exists at least one of: an (nonzero) eigenvector for A, or a 2-dimensional subspace (plane) invariant under A.
Length: 16:12

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