Why is $\det(e^X)=e^{\operatorname{tr}(X)}$?
11557
How to prove $\det(e^A) = e^{\operatorname{tr}(A)}$?
24072
Intuitive explanation of why $\dim\operatorname{Im} T + \dim\operatorname{Ker} T = \dim V$
127000
When does $V = \ker(f) \oplus \operatorname{im}(f)$?
69349
If $A$ is positive definite, then $\int_{\mathbb{R}^n}\mathrm{e}^{-\langle Ax,x\rangle}\text{d}x=\left|\det\left({\pi}^{-1}A\right)\right|^{-1/2}$
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
81181
Prove that $\det(M-I)=0$ if $\det(M)=1$ and $MM^T=I$
25009
$\operatorname{tr}(A)=\operatorname{tr}(A^{2})= \ldots = \operatorname{tr}(A^{n})=0$ implies $A$ is nilpotent
125348
Does $\det(A + B) = \det(A) + \det(B)$ hold?
67784
If $A + A^t = 2I$ then $\det(A) \geq 1$
83183
Why is $\langle x| x' \rangle=\delta(x-x')$?
87676
Why is determinant a multilinear function?
101452
How is the determinant related to the inverse of matrix?
128355
Does $e^{tx} + x = t - 1$ yield a solution/s to $\frac{dx}{dt} = \frac{e^{-tx} - x}{e^{-tx} + t}$?
122951
If the $\det(A)=0$ why does the matrix $A$ have an eigenvector?
53466
derivative of a determinant of matrix
22149
How to prove $dim(Ker (A- \lambda I))=dim (Ker(A^t- \lambda I))$?
67588
Why does $|e^{ix}|^2 = 1$?