A linear operator $T:V\rightarrow V$ has a cyclic vector iff $f_T=m_T$ (minimal polynomial=characteristic polynomial)
132059
Minimal polynomials and cyclic subspaces
11566
Similar matrices and minimal polynomial
109228
Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
7384
How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?
58572
Prove two commutative linear transformations on a vector space over an algebraically closed field can be simultaneously triangularized
132386
Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
137890
Diagonalizable Operators and characteristic polynomials
2439
If a linear operator has an adjoint operator, it is bounded
102935
Trace and determinant of composition of a left-multiplication and a right-multiplication on a space of matrices
48111
Invariant Subspace of Two Linear Involutions
93062
Is Every Invariant Subspace the Kernel of an polynomial applied in the operator?
6960
Necessary and sufficient condition for the matrix $A = I - 2 x x^t$ to be orthogonal
68526
Polynomials as vector spaces?
15811
Finding a basis for a certain vector space of periodic polynomials
82295
Showing that the minimal polynomial of an $n \times n$ matrix has degree at most $n$ without using the Cayley-Hamilton Theorem
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
48906
Prove that T is diagonalizable if and only if the minimal polynomial of T has no repeated roots.