Diagonalization matrix

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HanpenRobot

Diagonalization matrix memo

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Diagonalization matrix
Monday March 28 2016
Hanpen Robot

Let 𝔸 be a 2x2 square matrix
and 𝕧 𝜆1
, 𝕧 𝜆2
be a eigenvector of 𝔸.
Now consider a coordinate on 𝕧 𝜆1
, 𝕧 𝜆2
.
𝔸 𝑥𝕧 𝜆1
+ 𝑦𝕧 𝜆2
= 𝑥𝜆1 𝕧 𝜆1
+ 𝑦𝜆2 𝕧 𝜆2
∴
𝑥
𝑦 =
𝜆1 𝑥
𝜆2 𝑦
=
𝜆1 0
0 𝜆2
𝑥
𝑦

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