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Finance Quant Interview - IV

For what values of \( n \) does there exist complex \( n \times n \) matrices \( A, B \) such that

\[ A B - BA = Id? \]

Note by Calvin Lin
2 years, 6 months ago

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If d=0, the condition holds trivially for all n by taking A=B=I. If d is different from zero, taking trace of both sides and using the fact that tr(AB)=tr(BA), we conclude that none such n exists.

Abhishek Sinha - 2 years, 6 months ago

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Id means identity matrix.

Calvin Lin Staff - 2 years, 6 months ago

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Anyways, I took it as identity matrix times the scalar d.

Abhishek Sinha - 2 years, 6 months ago

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@Abhishek Sinha No issues. That's a more general case :)

Notation for identity matrix isn't standardized anyway. I was debating between I and Id.

Calvin Lin Staff - 2 years, 6 months ago

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