Comments on: Matrix $XY-YX$ Never Be the Identity Matrix https://yutsumura.com/matrix-xy-yx-never-be-the-identity-matrix/ Thu, 14 Dec 2017 16:04:22 +0000 hourly 1 https://wordpress.org/?v=5.3.4 By: Yu https://yutsumura.com/matrix-xy-yx-never-be-the-identity-matrix/#comment-4516 Thu, 14 Dec 2017 16:04:22 +0000 https://yutsumura.com/?p=1981#comment-4516 Note that the trace of the $n\times n$ identity matrix is $n$: $\tr(I)=n$.
By assumption, we have $XY-YX=I$. Combining these we have $n=tr(XY-YX)$.

]]> By: Lalitha https://yutsumura.com/matrix-xy-yx-never-be-the-identity-matrix/#comment-4507 Thu, 14 Dec 2017 12:56:07 +0000 https://yutsumura.com/?p=1981#comment-4507 Did we assume tr(XY−YX)=n in the proof?

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