For a real matrix A, the non-zero singular values are the square roots of the non-zero eigenvalues of which two matrices?

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A^T A and AA^T

The matrices A^T A and AA^T share the same non-zero eigenvalues, and the singular values of A are the square roots of those values. This relationship is the foundation of Singular Value Decomposition (SVD), a powerful tool used in image compression and Latent Semantic Analysis. Unlike eigenvalues, which only exist for square matrices, singular values are defined for every matrix.

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The non-zero singular values of a real matrix A are found by taking the square roots of the non-zero eigenvalues of which two product matrices?

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