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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.

- 2 years, 6 months ago

Id means identity matrix.

Staff - 2 years, 6 months ago

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

- 2 years, 6 months ago

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

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

Staff - 2 years, 6 months ago