1) Let L be the line through the origin of R2 that makes an angle of π/4 with the positive x-axis, and let A be the standard matrix for the reflection of R2 about that line. Make a conjecture about the eigenvalues and eigenvectors of A and confirm your conjecture by computing them in the usual way

Question

1)	Let L be the line through the origin of R2 that makes an angle of π/4 with the positive x-axis, and let A be the standard matrix for the reflection of R2 about that line. Make a conjecture about the eigenvalues and eigenvectors of A and confirm your conjecture by computing them in the usual way

turingtest · Answer

I'm not sure what kind of conjecture to make about this
I suppose it is reasonable to hypothesize that the eigenvectors will span $\mathbb R^2$
anyway, finding them is not hard
the line that intersects the x-axis at an angle of $\frac\pi4$ is $x=y$
what is the transformation for a point about that line?

turingtest · Answer

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