10 I believe your proof is correct. Note that the best way of proving that det(A) = det(At) det (A) = det (A t) depends very much on the definition of the determinant you are using. My personal …

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 …

In this way of looking at it, we see the result is equivalent to the observation that in even numbers of dimensions, changing the sign of everything can be achieved just by spinning everything …

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

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 …

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?

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 …

det(A)I d e t (A) I is a diagonal matrix with all entries equal to det(A) d e t (A). The determinant of a diagonal matrix can be found by multiplying the diagonal entries.

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 …

Writing out an arbitrary $2\times 2$ matrix and then slogging through a computation of $\det A$ and $\det A^\dagger$ is tedious, and it doesn't generalize to higher-dimensions.