Let w=(w_1, w_2) be a pair of positive real numbers with w_1+w_2=1 and w_1≥ w_2 . We show that the set of w -weighted singular vectors in R^2 has Hausdorff dimension 2- 1/1+w_1 . This extends the previous work of Yitwah Cheung on the Hausdorff dimension of the usual (unweighted) singular vectors in R^2 .
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Liao et al. (2019) studied this question.