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Projecting onto a line

MediumLinear Algebra~5m

The matrix projecting orthogonally onto the line spanned by v=(3,4)⊤v = (3, 4)^\top is P=vv⊤v⊤vP = \dfrac{vv^\top}{v^\top v}. What is its top-left entry?

Show hints (2)+
  1. P=vv⊤/(v⊤v)P = vv^\top / (v^\top v).
  2. v⊤v=25v^\top v = 25; the (1,1)(1,1) entry is 9/259/25.

Answer

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0.36 (± 0.01)

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