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\begin{bmatrix}0\\ 1\\ 0\\ 0\end{bmatrix}.
</math>
Thus, for the given matrix <math>W</math> with its column-space that is spanned by two exact left singular vectors, we determine these left singular vectors, as well as the corresponding rights singular vectors and the singular values, all exactly. For an arbitrary matrix <math>W</math>, we obtain approximate singular triplets which are optimal given <math>W</math> in the sense of optimality of the Rayleigh–Ritz method.
== Derivation from calculus of variations ==
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