As a step in a solution to another question our lecture notes claim that the matrix (a,b,c,d are real scalars).(adsbygoogle = window.adsbygoogle || []).push({});

\begin{bmatrix}

2a & b(1+d) \\

b(1+d)& 2dc \\

\end{bmatrix}

Is positive definite if the determinant is positive. Why? Since the matrix is symmetric it's positive definite if the it got positive (real) eigenvalues and ##det (A) = \prod \lambda_i## but two negative eigenvalues would give a positive determinant too.

Earlier in the text its given that the matrix

##

S =

\begin{bmatrix}

a & b \\

b& c \\

\end{bmatrix}

##

is positive definitive while ##d## is without any restrictions if that is somehow relevant.

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# Determinant and symmetric positive definite matrix

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