calculating eigenspaces
3,701
Solution 1
You can find the Eigenspace (the space generated by the eigenvector(s)) corresponding to each Eigenvalue by finding the kernel of the matrix $A\lambda I$. This is equivalent to solving $(A\lambda I)x=0$ for $x$.
In your case:
For $\lambda =1$ the eigenvectors are $(1,0,2)$ and $(0,1,3)$ and the eigenspace is $gen\{(1,0,2);(0,1,3)\}$ For $\lambda =2$ the eigenvector is $(0,2,5)$ and the eigenspace is $gen\{(0,2,5)\}$
Solution 2
Denote $A$ your matrix. To find the eigenspace of $\lambda$ solve for $X=(x,y,z)^T$ the equation $$AX=\lambda X$$
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Comments

user314159 6 months
how do you calculate eigenspaces?

user130512 almost 9 yearsFind vector solutions for (AI) = 0 and (A2I) = 0
