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Q 1) (25 pts) A projection matrix (or a projector) is a matrix P for which...

Q 1) (25 pts) A projection matrix (or a projector) is a matrix P for which P^2 = P.

a) (10 pts) Find the eigenvalues of a projector. Show details

b) (10 pts) Show that if P is a projector, then (I – P) is also projector. Explain briefly.

c) (5 pts) What assumption about matrix A should be made to run the power method?

Math   Advanced-Math   
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Answer #1

(c) The power method is very good at approximating the extremal eigenvalues
of the matrix, that is, the eigenvalues having largest and smallest module,
denoted by λ_1 and λ_n respectively, as well as their associated eigenvectors.In general, matrix A should be diagonalization matrix.

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