Week 7: Eigenvalues and Eigenvectors

1Iff if ti
F.IE ms.mn
If so findinvertable matrix P anddiagonal matrix D suchthat a PDP

so then
a it X o III x o

1 1
Iii 1 1
L
of i
11 of
eigenvector e

1
eigenvector

xp
p X X2
P
11 i A aeta

p a p




iiiiiti.it
D 1.1.12
Itil
1
E j.EE E n rane me gnatpproects
vectors ontothe plane
guys
o

competitive the
sol P T 8 foranynormalvectorw̅


LIFE pett foranyvectorw̅ ontheplane

Pn on o so thefirsteigenvalue is 0 ie x O

Anynormalvector totheplane is a scalarmultiple of 2 3 5 0
f1
so eigenvectorfort

Andds IsincePCJFI.iew̅
and o
einvectorsforntwillbeanytwolinearlyindependentvectorsontheplaneegfo.is 1.3s