View the step-by-step solution to:

Question

Screen Shot 2019-10-01 at 8.33.11 PM.pngHi, I was wondering how would

I approach this proof?

Screen Shot 2019-10-01 at 8.33.11 PM.png

(i) (4 points) Let a E R", c > 0, and
f (x) = a x+ cx x.
Show that f is coercive on Rn.
(You may assume linear functions and Euclidean norm are continuous.)
(ii) (6 points) Let C E Rnxn be a positive definite matrix, a E Rn, and
f (x) = a x+x Cx.
Show that f is coercive on Rn.
Hint: Use the Spectral Decomposition Theorem (see Theorem 2.4) from the lecture notes.
Also, as I mentioned in the class, positive semidefinite matrices and positive definite matrices are
symmetric (i.e., A = A ) by the way we defined them in the class. (See Definition 2.1. from the
lecture notes.)

Recently Asked Questions

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes