Hi, I am trying to figure this problem out, but I am having difficulty.
What I do know is that since A is symmetric, then S must be orthogonal. Also that S^(-1) must equal S^t (Transpose). However i am not sure how to piece this information together.
Thoughts?
What is $Av$? $(vv^T)v = v(v^Tv). v^Tv$ is a scalar and an eigenvalue of $A$. $v$ is an eigenvector.
Can we guess at any of the other eigenvectors? What about the remaining columns in R? Suppose $v_2$ is a column vector in $R$ (and is not v). Since R is normal $(v^T)(v_2) = 0$
S = R, and D has all zeroes along the main diagonals except in the first entry.