Given the following: $$\\ \begin{bmatrix}(adsbygoogle = window.adsbygoogle || []).push({});

A & 0\\

0 & B\\

\end{bmatrix}$$ the eigenvalues is exactaly A and B. So analogously, is possible to write a matrix with only two elements, T and D, such that the trace is T and the determinant is D?

I tried something: $$\\ \text{tr} \left(

\begin{bmatrix}

\frac{1}{2}T & 0\\

0 & \frac{1}{2}T\\

\end{bmatrix}

\right) = T $$

$$\\ \text{det} \left(

\begin{bmatrix}

\sqrt{\frac{D}{2}} & \sqrt{-\frac{D}{2}} \\

\sqrt{-\frac{D}{2}} & \sqrt{\frac{D}{2}} \\

\end{bmatrix}

\right) = D $$

But I can't join the 2 formulas...

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# How write a matrix in terms of determinant and trace?

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