'when eigenvectors share the same eigenvalue; how we can have a set of orthogonal vectors lying in their span?
I'm reading Chapter 2 of Deep learning book, and am not understanding the following satatement correctly:
A = Q Lambda QT
While any real symmetric matrix A is guaranteed to have an eigendecomposi-tion, the eigendecomposition may not be unique.
If any two or more eigenvectors share the same eigenvalue, then any set of orthogonal vectors lying in their span are also eigenvectors with that eigenvalue, and we could equivalently choose a Q using those eigenvectors instead.
How this could be possible? To have an orthogonal vector in span of two already orthogonal vector!?
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