A矩阵的 行列式 （determinant），用符号det (A)表示。 行列式在数学中，是由解 线性方程组 产生的一种算式其 定义域 为nxn的矩阵 A，取值为一个 标量，写作det (A)或 | A | 。行列式可以看 …

10 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 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 …

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 …

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 …

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

Apr 14, 2014 · $det (A)I$ is a diagonal matrix with all entries equal to $det (A)$. The determinant of a diagonal matrix can be found by multiplying the diagonal entries. So, we get the result.

Jul 12, 2016 · That actually makes sense to me now. Thank you for your assistance!

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 …

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 …