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 …

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 …

Aug 1, 2013 · When $A$ is a $n \times n$ matrix, the above expansion terminate at the $t^n$ term with coefficient equal to $\det A$. With this, you can obtain formula similar to what you …

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 …

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 …

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 …

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 …

Feb 10, 2019 · How do I go about solving this? The $\det (3A)$ is not simply $3\cdot\frac {1} {8}$ correct?

Sep 6, 2022 · Prove $$\\det \\left( e^A \\right) = e^{\\operatorname{tr}(A)}$$ for all matrices $A \\in \\mathbb{C}^{n \\times n}$.

Mar 8, 2024 · A short index-free proof can be given using the identity 2det (A) = (tr A)^2- tr (A^2) (which can be checked by writing det and tr in terms of eigenvalues) and linearity of trace.