Exercise 6.5

Let P ∈ ℂm×n be a nonzero projector. Show that ∥P∥2 ≥ 1, with equality if and only if P is an orthogonal projector.

Answers

PIC

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2019-06-05 00:00
Comments
  • What if x is not in the range of the projector? Also, if Px = (lamda)x =P^2 x = (lamda^2)x, then shouldn’t the spectral norm be 1 for all projectors since the eigenvalues can only be 0 or 1? How can you be sure that the singular values are all 1. Take this example matrix: [[1,0,0],[0,1,0],[0,0,0]]
    Varun • 2025-01-13