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ml-recall

#normal-equation

3 questions from Linear Models & Regularization

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3 questions · 3 min · score and explanations at the end

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Question 1: Short answer

mediumAI-checkedLinear Models & Regularization

A design matrix XX has (2-norm) condition number κ(X)=σmax⁡/σmin⁡=103\kappa(X) = \sigma_{\max}/\sigma_{\min} = 10^3, the ratio of its largest to smallest singular value. You solve least squares through the normal equations, i.e. you form and solve with X⊤XX^\top X. What is the condition number of X⊤XX^\top X?

a number, e.g. 1e4