How to prove $\\operatorname{Tr}(AB) = \\operatorname{Tr}(BA)$?
Jan 11, 2015 · 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
$AB-BA=I$ having no solutions - Mathematics Stack Exchange
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$A^2=AB+BA$. Prove that $\\det(AB-BA)=0$
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matrices - When will $AB=BA$? - Mathematics Stack Exchange
Aug 29, 2013 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
linear algebra - Does $\det (A + B) = \det (A) + \det (B)$ hold ...
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The commutator of two matrices - Mathematics Stack Exchange
The commutator [X, Y] of two matrices is defined by the equation $$\begin{align} [X, Y] = XY − YX. \end{align}$$ Two anti-commuting matrices A and B satisfy $$\begin{align} A^2=I \qu...
Proofs of determinants of block matrices [duplicate]
I know that there are three important results when taking the Determinants of Block matrices $$\\begin{align}\\det \\begin{bmatrix} A & B \\\\ 0 & D \\end ...
Show that $ e^{A+B}=e^A e^B$ - Mathematics Stack Exchange
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linear algebra - How to show that $\det(AB) =\det(A) \det(B ...
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If eigenvalues are positive, is the matrix positive definite?
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