Why is rank $uv^{T}$ always equal to 1?
97487
How to prove whether a matrix has rank $1$
77137
The rank of Jacobian matrix at a point of affine variety is independent of choice of generators
86919
When (and more importantly, why) does $AA^T$ have an inverse?
45261
Why is the determinant of a rotation matrix equal to 1?
81240
Norm of an inverse operator: $\|T^{-1}\|=\|T\|^{-1}$?
74187
$\operatorname{ord}(u)=r,\,\operatorname{ord}(v)=s$ $\,\Rightarrow\,\operatorname{ord}(uv)=rs\,$ if $\,r,s\,$ (co)primes
86084
Why is $T$ normal and idempotent?
46128
Representation of Matrix with Rank 1
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$
76200
Is the rank of $AB$ always equal to the rank of $BA$?
1162
Why $\{\mathbf{0}\}$ has dimension zero?
71604
Why is the determinant of the 0x0 matrix equal 1?
42265
A proof that $\displaystyle\sum_{i=1}^{n}P''(r_i)/P'(r_i)=0$ for a degree $n$ polynomial
52621
Why is $\det(A - \lambda I)$ zero?
117383
What is the value of $\Gamma(\mathrm{i})$ ?
15197
Relation between trace and rank for projection matrices
156877
Rank-one perturbation proof