#### Rodrigo_pn

##### New member

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Thank you

- Thread starter Rodrigo_pn
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Thank you

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Where did the A come from? It's just \(\displaystyle \Delta\). A typo maybe?

Thank you

Anyway, a diagonal matrix commutes with anything so

\(\displaystyle U^TPU \Delta + \Delta U^TPU = U^TPU \Delta + U^TPU \Delta = \left ( U^TPU + U^TPU \right ) \Delta = -I\)

Can you finish?

-Dan

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Yes, it is a typo.Where did the A come from? It's just \(\displaystyle \Delta\). A typo maybe?

Anyway, a diagonal matrix commutes with anything so

\(\displaystyle U^TPU \Delta + \Delta U^TPU = U^TPU \Delta + U^TPU \Delta = \left ( U^TPU + U^TPU \right ) \Delta = -I\)

Can you finish?

-Dan

In place of matrix A is

\(\displaystyle \Delta\)

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Thank you

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Please show us how far you progressed with that hint.

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The continuation: \(\displaystyle U^TPU\Delta+\Delta{U^TPU}=-I\)

Please show us how far you progressed with that hint.

\(\displaystyle U^TPU\Delta+U^TPU\Delta = -I\)

\(\displaystyle U^{-T}[2U^TPU\Delta=-I]U^{-1}\Delta^{-1}\)

\(\displaystyle P=-\dfrac{1}{2}U^{-T}U^{-1}\Delta^{-1}\)

\(\displaystyle P=-\dfrac{1}{2}U^{-T}\Delta^{-1}{U^{-1}}\)

\(\displaystyle P=-\dfrac{1}{2}(U\Delta{U^T})^{-1}\)