- #1

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,the diagonal form of A is [tex]D=\left(\begin{array}{cc}a & 0\\0 & b\end{array}\right)[/tex]

i got weird numbers so for convinience the eigenvalues are a,b

so there is U for which

[tex]U^{-1}AU=\left(\begin{array}{cc}a^{\frac{1}{3}} & 0\\0 & b^{\frac{1}{3}}\end{array}\right)^{3}[/tex]

i can find U

because A is simetric so U is consists of the orthonormal eigenvectors of A

what to do next,how to find B

?