I have recently seen use of the following identity:
$ ADA^T = D A^T A $ where A is a real rectangular matrix and D is a real diagonal matrix.
Does this necessarily hold? Or is it the other way around? I thank all helpers.
2026-04-03 23:17:11.1775258231
An identity for diagonal matrices
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I think that what you have seen is associated with "trace" function; more precisely, it is likely to be a particular case of the cyclic invariance of the trace:
$$trace(A*B*C)=trace(B*C*A)$$
see (https://en.wikipedia.org/wiki/Trace_(linear_algebra))