query: Find all complex matrices $A$ such that $n\operatorname{Tr}(AB) = \operatorname{Tr}(A)\operatorname{Tr}(B)$ for all $B$.
positive_passages.docid: 142097
positive_passages.text: Finding the dimension of the orthogonal complement
negative_passages.docid: 121062
negative_passages.text: Given a matrix, is there always another matrix which commutes with it?
negative_passages.docid: 11566
negative_passages.text: Similar matrices and minimal polynomial
negative_passages.docid: 30889
negative_passages.text: Classifying complex $2\times 2$ matrices up to similarity
negative_passages.docid: 95227
negative_passages.text: Is the set of all $n\times n$ matrices, such that for a fixed matrix B  AB=BA, a subspace of the vector space of all $n\times n$ matrices?
negative_passages.docid: 58021
negative_passages.text: Finding matrix $B$ is not zero matrix where $AB= 0$
negative_passages.docid: 90475
negative_passages.text: Coordinate-free proof of $\operatorname{Tr}(AB)=\operatorname{Tr}(BA)$?
negative_passages.docid: 55062
negative_passages.text: $2\times 2$ matrix $C=AB-BA$
negative_passages.docid: 86841
negative_passages.text: Find a matrix $B$ such that $B^3 = A$
negative_passages.docid: 110086
negative_passages.text: Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
negative_passages.docid: 8920
negative_passages.text: There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
negative_passages.docid: 63753
negative_passages.text: Eigenvalues of product of two complex matrices
negative_passages.docid: 84626
negative_passages.text: Why in these matrices are $AB=BA$ not equal? What is the logic behind them?
negative_passages.docid: 110408
negative_passages.text: Solving for $A$ in $Ax = b$
negative_passages.docid: 123044
negative_passages.text: Commutative matrices are multiples of the identity
negative_passages.docid: 18145
negative_passages.text: Diagonalizable matrices with complex values are dense in set of $n\times n$ complex matrices.
negative_passages.docid: 105996
negative_passages.text: Topology of matrices