query: $AB - BA = \lambda B$ has a nontrivial solution, iff $\lambda = \lambda_i - \lambda_j$?
positive_passages.docid: 150228
positive_passages.text: If $E$ has eigenvalues $\lambda_1, \ldots, \lambda_n$, then $B \mapsto [E,B] = EB - BE$ has eigenvalues $\lambda_i - \lambda_j$.
negative_passages.docid: 85540
negative_passages.text: Prove or Disprove the Existence of Solutions...
negative_passages.docid: 13346
negative_passages.text: If $A=AB-BA$, is $A$ nilpotent?
negative_passages.docid: 27899
negative_passages.text: Can we prove the existence of $A\cup B$ without the union axiom?
negative_passages.docid: 8638
negative_passages.text: If I know $AB$, how can I calculate $BA$?
negative_passages.docid: 35874
negative_passages.text: Show that when $BA = I$, the solution of $Ax=b$ is unique
negative_passages.docid: 58021
negative_passages.text: Finding matrix $B$ is not zero matrix where $AB= 0$
negative_passages.docid: 131844
negative_passages.text: When does $(e^a)^b = e^{ab}$ hold?
negative_passages.docid: 151332
negative_passages.text: If $A,B$ have eigenvalues $\pm1$, what can I say about the eigenvalues of $AB,BA$?
negative_passages.docid: 25882
negative_passages.text: Is this algebraic identity obvious? $\sum_{i=1}^n \prod_{j\neq i} {\lambda_j\over \lambda_j-\lambda_i}=1$
negative_passages.docid: 34973
negative_passages.text: Is it true that the order of $ab$ is always equal to the order of $ba$?
negative_passages.docid: 36998
negative_passages.text: In $Ax=b$. If $A$ is not invertible there are no solutions or infinity. How to determine what the case is?
negative_passages.docid: 49330
negative_passages.text: If for two suitable matrices $B$ and $C$, $AA^TB=AA^TC$ can we conclude that $A^TB=A^TC$?
negative_passages.docid: 66709
negative_passages.text: Are the matrix products $AB$ and $BA$ similar?
negative_passages.docid: 15626
negative_passages.text: Relations of a~b iff b = ak^2
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
negative_passages.docid: 6096
negative_passages.text: If $A+B=AB$ then $AB=BA$