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Everyone knows that for any two square matrices $A$ and $B$ (with coefficients in a commutative ring) that $$tr(AB) $\operatorname{tr}(AB) = tr(BA).$$\operatorname{tr}(BA).$$ I once thought that this implied (via induction) that the trace of a product of any finite number of matrices was independent of the order they are multiplied. |
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1 | [made Community Wiki] | ||
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Everyone knows that for any two square matrices $A$ and $B$ (with coefficients in a commutative ring) that $$tr(AB) = tr(BA).$$ I once thought that this implied (via induction) that the trace of a product of any finite number of matrices was independent of the order they are multiplied. |
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