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You are given a very large symmetric matrix 𝐴 A that doesn’t fit into memory, 𝐴 ∈ 𝑅 1 𝑀 × 1 𝑀 A∈R 1M×1M , and a function 𝑓 ( 𝑥 ) = 𝐴 𝑥 f(x)=Ax that can quickly compute 𝑓 ( 𝑥 ) f(x) for 𝑥 ∈ 𝑅 1 𝑀 x∈R 1M . How would you find the unit vector 𝑥 x that minimizes 𝑥 𝑇 𝐴 𝑥 x T Ax?

Machine Learning Intern

Interviewed at Anonymous

3.4★
Dec 31, 2024

You are given a very large symmetric matrix 𝐴 A that doesn’t fit into memory, 𝐴 ∈ 𝑅 1 𝑀 × 1 𝑀 A∈R 1M×1M , and a function 𝑓 ( 𝑥 ) = 𝐴 𝑥 f(x)=Ax that can quickly compute 𝑓 ( 𝑥 ) f(x) for 𝑥 ∈ 𝑅 1 𝑀 x∈R 1M . How would you find the unit vector 𝑥 x that minimizes 𝑥 𝑇 𝐴 𝑥 x T Ax?

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