How do I prove that $\det A= \det A^T$? - Mathematics Stack …
9 I believe your proof is correct. Note that the best way of proving that $\det (A)=\det (A^t)$ depends very much on the definition of the determinant you are using. My personal favorite …
海运中DEM与DET分别代表什么？所谓的免堆与免用？所谓场内场 …
Aug 6, 2024 · 海运中，DEM和DET是两种常见的费用术语。DEM代表滞期费（Demurrage Charges），当船舶在港口停留超过预定时间，未能及时卸货或装货，船东会向租船人收取这 …
linear algebra - Why is $\det (-A)= (-1)^n\det (A)
Typically we define determinants by a series of rules from which $\det (\alpha A)=\alpha^n\det (A)$ follows almost immediately. Even defining determinants as the expression used in …
prove that $\det (ABC) = \det (A) \det (B) \det (C)$ [for any $n×n ...
Feb 7, 2020 · I was thinking about trying to argue because the numbers of a given matrix multiply as scalars, the determinant is the product of them all and because the order of the …
linear algebra - How to prove $\det \left (e^A\right) = e ...
Sep 6, 2022 · Prove $$\\det \\left( e^A \\right) = e^{\\operatorname{tr}(A)}$$ for all matrices $A \\in \\mathbb{C}^{n \\times n}$.
The determinant of adjugate matrix - Mathematics Stack Exchange
Jan 17, 2016 · Thus, its determinant will simply be the product of the diagonal entries, $ (\det A)^n$ Also, using the multiplicity of determinant function, we get $\det (A\cdot adjA) = \det …
linear algebra - How to show that $\det (AB) =\det (A) \det (B ...
Aug 28, 2011 · Once you buy this interpretation of the determinant, $\det (AB)=\det (A)\det (B)$ follows immediately because the whole point of matrix multiplication is that $AB$ corresponds …
$\det (I+A) = 1 + tr (A) + \det (A)$ for $n=2$ and for $n>2$?
Aug 1, 2013 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation …
Why $\det (A^ {-1}) = 1/\det (A)$? - Mathematics Stack Exchange
Jul 12, 2016 · Why $\det (A^ {-1}) = 1/\det (A)$? Ask Question Asked 9 years, 3 months ago Modified 4 years ago
linear algebra - Does $\det (A + B) = \det (A) + \det (B)$ hold ...
Feb 20, 2015 · It would be a good exercise to determine for which matrices, the identity $\det (A+b)=\det (A)+\det (B)$ holds. I think that it would work for rather few of them.