A is a simetric metrices nxn. so [tex]v\in R^n[/tex] and [tex]v\neq 0[/tex](adsbygoogle = window.adsbygoogle || []).push({});

so [tex](\lambda I -A)^2=0[/tex] for some [tex]\lambda[/tex]

prove that for the same [tex]v[/tex] [tex](\lambda I -A)=0[/tex]

how i tried to solve it:

i just collected data from the given.

simetric matrices is diagonizable.

[tex]B=(\lambda I -A)[/tex]

we were given that [tex]B^2v=0[/tex]

so [TEX]B^2v \bullet v=0[/TEX] (dot product is also v)

so v is orthogonal to [TEX]B^2v[/TEX]

what to do now?

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# Eigenvalue Problem

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