This preview shows page 1. Sign up to view the full content.
Unformatted text preview: x V we have M x V ). d) Show that V j is an invariant subspace for M . e) Show that V j V k = { } if j 6 = k . f) Denote by 1 ,..., k the distinct eigenvalues of M (in other words, { 1 ,..., k } = { 1 ,..., n } ). Show that M is diagonalizable in F n if and only if V 1 ... V k = F n and explain why the sum before is a direct sum. 2. Find the eigenspaces of the matrix A = 2 1 0 2 Is the matrix diagonalizable? 1...
View Full
Document
 Winter '08
 un
 Math, Linear Algebra, Algebra

Click to edit the document details