- Matrices - Conditions for $AB+BA=0$ - Mathematics Stack Exchange
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- $A^2=AB+BA$. Prove that $\\det(AB-BA)=0$ - Mathematics Stack Exchange
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- How to prove $\\operatorname{Tr}(AB) = \\operatorname{Tr}(BA)$?
The efficient @hjhjhj57: answer $$\text{Tr}(AB) = \text{Tr}(BA)= \sum a_{ij} b_{ji}$$ Now we can start to understand why if we do a circular permutation of the factors the expression
- How to calculate total combinations for AABB and ABBB sets?
Although both belong to a much broad combination of N=2 and n=4 (AAAA, ABBA, BBBB ), where order matters and repetition is allowed, both can be rearranged in different ways: First one: AABB, BBAA, ABAB, BABA, ABBA, BAAB (6 possible combinations) Second one: ABBB, BABB, BBAB, BBBA (4 possible combinations)
- How to show that - Mathematics Stack Exchange
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- Find a generating function for the number of strings
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- sequences and series - The Perfect Sharing Algorithm (ABBABAAB . . .
AB -> ABBA -> ABBABAAB This allowed me to get a computer to achieve the algorithm in many ways, but it also raised some questions Question 1: Can I repeat this forever and have it properly generate the algorithm? The algorithm is normally created by taking AB, then inverting each 2-state 'digit' and sticking it on the end (ABBA)
- Is $AB+BA$ positive definite too if $A$ and $B$ are positive definite?
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