MATH 3620 Lecture 4: CH9_ Indirect Method of Finding Eigenvalues

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Review of Linear Algebra Concepts
(Section 9.1)
Section 9.1
linear independence:
Óv(1),...,v(k)Ôis linearly independent if
c1v(1) +···+ckv(k)=0c1=··· =ck=0
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basis for Rn:
nlinearly independent vectors in RnOR nvectors that span Rn
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Theorem 9.3:
If Óv(1),...,v(n)Ôis a basis for Rn, then for any xœRnthere exist unique scalars
c1,...,c
nsuch that
x=c1v(1) +···+cnv(n)
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complete eigenvalue:
dim(N(AI)) = multiplicity of
defective eigenvalue:
dim(N(AI)) <multiplicity of
Ais invertible if and only if =0is NOT an eigenvalue of A
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