Suppose that \(\{u_i\}_{i=1}^m\) is a set of orthonormal vectors, such that principal semiaxes of the hyperellipse are \(\{\sigma_i u_i\}\text{.}\) These scalars \(\sigma_1, \sigma_2, \dots, \sigma_m\) are the singular values of \(A\), and encapsulate many important properties of \(A\text{.}\)
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