Characteristic polynomial and minimal polynomial of a linear operator $T$ coincide
62237
Characteristic polynomial equals minimal polynomial iff $x, Mx, \ldots, M^{n-1} x$ are linearly independent
7813
In a complex vector space, $\langle Tx,x \rangle=0 \implies T = 0$
6960
Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
152887
Let $T : V \rightarrow V$ be a linear operator. If $T^n = O_V$ for some $n \ge 1$, prove that $I_V + T$ is an isomorphism.
93062
Is Every Invariant Subspace the Kernel of an polynomial applied in the operator?
111248
The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
144097
eigenvalues and eigenvectors of $vv^T$
128361
The kernel and range of the powers of a self-adjoint operator
81040
proof about commutative operators and T-cyclic vectors
79276
Find $\min(\operatorname{trace}(AA^T))$ for invertible $A_{n\times n}$
52528
Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
66409
Show that the linear operator $(Tf)(x)=\frac{1}{\pi} \int_0^{\infty} \frac{f(y)}{(x+y)} dy$ satisfies $\|T\|\leq 1$.
60655
$\ker T\subset \ker S\Rightarrow S=rT$ when $S$ and $T$ are linear functionals
132059
Minimal polynomials and cyclic subspaces
48906
Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots.
66481
Convergence of characteristic functions to $1$ on a neighborhood of $0$ and weak convergence
32606
Is the operator $T((x_1,x_2,...,x_n))=(x_1,\frac{x_2}2,\frac{x_3}3,...)$ on $\ell^2$ self-adjoint and unitary