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- How many $4$-digit palindromes are divisible by $3$?
How many 4 4 -digit palindromes are divisible by 3 3? I'm trying to figure this one out I know that if a number is divisible by 3 3, then the sum of its digits is divisible by 3 3 All I have done is listed out lots of numbers that work I haven't developed a nice technique for this yet
- How to prove $\\operatorname{Tr}(AB) = \\operatorname{Tr}(BA)$?
there is a similar thread here Coordinate-free proof of $\operatorname {Tr} (AB)=\operatorname {Tr} (BA)$?, but I'm only looking for a simple linear algebra proof
- matrices - When will $AB=BA$? - Mathematics Stack Exchange
Given two square matrices A, B A, B with same dimension, what conditions will lead to this result? Or what result will this condition lead to? I thought this is a quite simple question, but I can find little information about it Thanks
- linear algebra - Does $\det (A + B) = \det (A) + \det (B)$ hold . . .
Can there be said anything about det(A + B) det (A + B)? If A B A B are symmetric (or maybe even of the form λI λ I) - can then things be said?
- 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 amp; B \\\\ 0 amp; D \\end
- How to show that $\\det(AB) =\\det(A) \\det(B)$?
Given two square matrices $A$ and $B$, how do you show that $$\det (AB) = \det (A) \det (B)$$ where $\det (\cdot)$ is the determinant of the matrix?
- Show that $ e^{A+B}=e^A e^B$ - e^ {A+B}=e^A e^B$ - Mathematics Stack . . .
As a remark, it is actually legitimate to assume that A A and B B are simultaneously diagonalisable (surprise, surprise!), so the proposition is trivial But obviously, the reason why we can make such an assumption is way beyond the scope of undergraduate (or even graduate) linear algebra courses
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