Eigenvalues of Correlation Matrix are Non-Negative

Definition

Let $\sequence a_n$ and $\sequence b_n$ be sequences of $n$ observations.

Let $\mathbf C$ be the correlation matrix with respect to $\sequence a_n$ and $\sequence b_n$.

Then the eigenvalues of $\mathbf C$ are non-negative.

Proof

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Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): correlation matrix