For unlimited access to Class Notes, a Class+ subscription is required.

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)=0∆c1=··· =ck=0

p572

basis for Rn:

nlinearly independent vectors in RnOR nvectors that span Rn

p572

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)

p572

complete eigenvalue:

dim(N(A≠⁄I)) = multiplicity of ⁄

defective eigenvalue:

dim(N(A≠⁄I)) <multiplicity of ⁄

Ais invertible if and only if ⁄=0is NOT an eigenvalue of A