Ivan Shishkin, Birch Grove

Spectral Theorem

Theorem / Euclidean vector space /

English
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In finite dimension, a real self-adjoint operator can be diagonalized in a unitary basis.

Practice this concept with exercises

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  • Show that if A∈Sn(R)A\in S_{n}(\mathbb{R}), AA is positive (resp. definite positive) if and only if all its eigenvalues are positive (resp. strictly positive)

    Open exercise
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