AdvancedMultiple choice
Keeping the big singular values · Part 3 of 3
A centred data matrix has singular values 5, 3 and 1, and no others. You want a low-rank summary of it.
You solve least squares with as the design matrix. What is its condition number, and what happens if you form explicitly?
- A5; forming XᵀX leaves it unchanged, because the same singular vectors appear
- B5; forming XᵀX squares it to 25
- C35, the ratio of the total to the smallest squared singular value
- D√5; forming XᵀX raises it to 5, the ratio of the singular values
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