Why is $T$ normal and idempotent?
101467
Let $T:V\to V$ be a linear map, where $V$ is an inner product space. Given $T^2=\frac{T+T^*}{2}$, prove that $T$ is normal and that $T=T^2$.
145104
$T:$ $\mathbb{C}$ $\to$ $\mathbb{C}$ by $T(z)=\lambda z + \mu \bar{z}$ for every $z \in \mathbb{C}$
12802
Proof of correctness of normal equation
131701
Why is $A^TA$ invertible if $A$ has independent columns?
94378
Is Linear transformations $T_1,T_2 : \mathbb{R}^n\rightarrow \mathbb{R}^n$ Invertible?
87494
$\operatorname{rank}(T^3) + \operatorname{rank}(T) \geq 2\operatorname{rank}(T^2)$ for finite-dimensional $V$
31113
Why is normal ordering a valid operation?
1119
A normal divided by the $\sqrt{\chi^2(s)/s}$ gives you a t-distribution -- proof
117546
Idempotent of closure and other properties
147611
Given $P$ idempotent, show that $I-P$ is idempotent.
12293
Let X be a T1 space, and show that X is normal if and only if each neighbourhood of a closed set F contains the closure of some neighbourhood of F
152853
What is the intuition behind the unit normal vector being the derivative of the unit tangent vector?
134402
$\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$ for $A$ idempotent matrix
112707
Must $Q^\mathsf{T}Q = I$ if $(Qx)^\mathsf{T}(Qx) = x^\mathsf{T}x$
66134
Sufficiently many idempotents and commutativity
112297
Normal + Connected -> Uncountable
49122
Why commutator subgroup is normal to G?