Set 3
... where V is a vector. Note that F (0) = V . Find the vector V and the matrix A that describe each of the following mappings [here the light blue F is mapped to the dark red F ]. ...
... where V is a vector. Note that F (0) = V . Find the vector V and the matrix A that describe each of the following mappings [here the light blue F is mapped to the dark red F ]. ...
Eigenvalues and Eigenvectors
... If (,p) is an eigenpair of A, then for any positive integer r, (r,p) is an eigen pair of Ar. Proof: Since (,p) is an eigenpair of A then Ap = p. Thus we have A2p = A(Ap) = A(p) = (Ap) = (p) = 2p, A3p = A(A2p) = A(2p) = 2(Ap) = 2(p) = 3p, and in general Arp = A(Ar-1p) = A(r-1p) = r-1( ...
... If (,p) is an eigenpair of A, then for any positive integer r, (r,p) is an eigen pair of Ar. Proof: Since (,p) is an eigenpair of A then Ap = p. Thus we have A2p = A(Ap) = A(p) = (Ap) = (p) = 2p, A3p = A(A2p) = A(2p) = 2(Ap) = 2(p) = 3p, and in general Arp = A(Ar-1p) = A(r-1p) = r-1( ...
Exam 3
... Problem 2: (15 points) True/False. If the statement is always true, mark true. Otherwise, mark false. You do not need to show your work. (Any work will not be graded.) (a) There exists a real 2 × 2 matrix, A, with eigenvalues λ1 = 1, λ2 = i. (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 fo ...
... Problem 2: (15 points) True/False. If the statement is always true, mark true. Otherwise, mark false. You do not need to show your work. (Any work will not be graded.) (a) There exists a real 2 × 2 matrix, A, with eigenvalues λ1 = 1, λ2 = i. (b) If λ = 2 is a repeated eigenvalue of multiplicity 2 fo ...
UNIVERSITY OF OSLO Faculty of mathematics and natural sciences
... Faculty of mathematics and natural sciences Examination in ...
... Faculty of mathematics and natural sciences Examination in ...