Given A is $m\times n$ and B is a $n \times m$ matrix, can we say trace(AB) = trace(BA)? It worked for a few examples with $m = 2$ and $n = 3$.
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It's generally true. Just write out the definition of the matrix product and the trace. See also this answer. – AnotherTest Feb 20 '17 at 10:11
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Yes, It is true. Trace(AB) = Trace(BA) for rectangular matrices. You can rewrite the expression used for calculating trace to prove this.
tr(AB) = $\sum_{i=1}^{m}(AB)_{ii} = \sum_{i=1}^{m}\sum_{j=1}^{n}A_{ij}B_{ji} = \sum_{j=1}^{n}\sum_{i=1}^{m}B_{ji}A_{ij} = \sum_{j=1}^{n}(BA)_{jj} $= tr(BA)
For more references, you can see the answers in this link : Read more here..
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While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review – Sarvesh Ravichandran Iyer Feb 20 '17 at 11:49
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