Timeline for When does a multiplicative subset of matrices have positive trace?

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Dec 17, 2022 at 4:04	history	edited	Isaiah Siegl	CC BY-SA 4.0	added 520 characters in body
Dec 17, 2022 at 0:21	comment	added	Aaron Meyerowitz		One sufficient condition is that there is some real matrix $P$ so that $PA_iP^{-1}$ is upper triangular with non-negative diagonal entries for each $i$.
Dec 16, 2022 at 22:30	comment	added	Joseph Van Name		Recall that if $A$ is a complex matrix, then $\overline{A}$ is the matrix obtained from $A$ by replacing each entry with its complex conjugate. i.e. $\overline{A}=(A^T)^*$. If $A_1,\dots,A_r$ are complex matrices, then every product $A_{i_1}\otimes\overline{A_{i_1}},\dots,A_{i_n}\otimes\overline{A_{i_n}}$ has real non-negative trace. Furthermore, in quantum information theory, the completely positive superoperators can be put into a linear one-to-one correspondence with the sums of the form $A_1\otimes\overline{A_1}+\dots+A_r\otimes\overline{A_r}$.
S Dec 16, 2022 at 20:29	review	First questions
Dec 17, 2022 at 8:40
S Dec 16, 2022 at 20:29	history	asked	Isaiah Siegl	CC BY-SA 4.0