Showing $\vert \mathrm{det}(A) \vert \le \prod_{j=1}^n \Vert a_j \Vert_2$
91740
Hadamard's inequality proof
102398
Help deriving that $\mathrm{sign} : S_n\to \{\pm 1\}$ is multiplicative
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
34702
Show $|A + uv^T| = (1 + v^T A^{-1} u) |A|$
129743
$A$ be a $2\times 2$ real matrix with trace $2$ and determinant $-3$
68538
Show that if $ A(t) \in \mathbb{R ^{n×n}}$ is a differentiable function of $t$ then $\frac{d(det A(t))}{dt}$
136652
Closed form expression for the product $\prod\limits_{k=1}^{n}\left(1 - \frac{1}{ak}\right)$
7802
Showing $\prod\limits_{i<j} \frac{x_i-x_j}{i-j}$ is an integer
101313
Minimal polynomial, determinants and invertibility
20467
Show that $(y_n)\in l^q$
20331
Determinant of a $2\times 2$ block matrix
56311
Proving $(1+a_{2})^{2}(1+a_{3})^{3}\cdots(1+a_{n})^{n}\ge n^n$ for positive reals $a_2,\ldots, a_n$ whose product is $1$
135252
If $M$ is positive definite, then $\operatorname{det}{(M)}\leq \prod_i m_{ii}$
101861
How do you prove that $tr(B^{T} A )$ is a inner product?
95266
Show $|t|\leq \pi \Rightarrow |e^{it}-1|\geq 2|t|/ \pi$
60900
If $A^2=-I$, Prove that $\det{A}=1$
109760
Showing that the product of all $n$th Roots of Unity is $(-1)^{n+1}$