Classify the following equation and reduce it to canonical form: yUxx-xUyy=0 , x>0 , y>0

Classify the following equation and reduce it to canonical form:

yUxx-xUyy=0 , x>0 , y>0

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Expert Solution

Colby Messinger answered 1 year ago

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Let \( A\in M_n(\mathbb{R})\hspace{2mm} \) and \( \hspace{2mm}\lambda_1, \lambda_2,...,\lambda_n \hspace{2mm} \)(no need distinct) be eigenvalues of A. Show that a). \( \sum _{i=1}^n\lambda _i=tr\left(A\right) \) b). \( \:\prod _{i=1}^n\lambda _i=\left|A\right|\: \)

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