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Unformatted text preview: ECEN 601: Assignment 9 Problems: 1. Show that for a square matrix F satisfying bardbl F bardbl < 1 for a norm satisfying the submultiplicative property, bardbl ( I F )- 1 bardbl 1 1 bardbl F bardbl . Hint: Use the Neumann expansion. 2. Show that if bardbl bardbl is a norm satisfying the submultiplicative property and F is a matrix with bardbl F bardbl < 1, then I F is non-singular. Hint: If I F is singular, there is a vector x such that ( I F ) x = . 3. Show for a square matrix F with bardbl F bardbl < 1, where the norm satisfies the submultiplicative property, that bardbl I ( I F )- 1 bardbl bardbl F bardbl 1 bardbl F bardbl . Hint: Show that I ( I F )- 1 = F ( I F )- 1 . 4. Show that for m m matrices A and B , bardbl AB bardbl F bardbl A bardbl 2 bardbl B bardbl F . Hint: Start by showing that bardbl AB bardbl 2 F = tr( B H A H AB )....
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This note was uploaded on 09/26/2011 for the course ECEN 601 taught by Professor Staff during the Fall '08 term at Texas A&M.
- Fall '08