Let $A\in\Bbb{K}^{n\times n}$ and $\mu_A$ the minimal polynomial of $A$. How can I show that $A$ is invertible and only if $\mu_A(0)\neq0$?
65305
Minimal polynomial for an invertible matrix and its determinant
112045
A property of minimal prime ideal
57771
Let $A\in M_{n\times n}(\Bbb R)$ so that $I\notin span(A,A^2,...,A^n)$. Prove that $\det(A)=0$.
135511
$M_a =\{ f\in C[0,1] |\ f(a)=0 \}$ for $a$ $\in$ $[0,1]$. Is $M_a$ finitely generated in $C[0,1]$?
7833
Ideal and minimal polynomial
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
65162
Show that $\dim H^0(\mathbb{P}^n, \mathcal{O}_{\mathbb{P}^n}(m)) = {n + m \choose n}$ if $m \geq 0$, and $0$ otherwise.
118916
How do I prove that a polynomial F[x] of degree n has at most n roots
156671
Necessary and sufficient condition for $x^n - y^m$ to be irreducible in $\Bbb C[x,y]$
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
32108
$ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$
132492
If a linear transformation $T$ has $z^n$ as the minimal polynomial, there is a vector $v$ such that $v, Tv,\dots, T^{n-1}v$ are linearly independent
156034
sufficient condition for a polynomial to have roots in $[0,1]$
119452
Nilpotent matrices with same minimal polynomial and nullity
148946
If $\mathbf{A}$ is a $2\times 2$ matrix that satisfies $\mathbf{A}^2 - 4\mathbf{A} - 7\mathbf{I} = \mathbf{0}$, then $\mathbf{A}$ is invertible
62237
Characteristic polynomial equals minimal polynomial iff $x, Mx, \ldots, M^{n-1} x$ are linearly independent
19280
Jordan Canonical Form determined by characteristic and minimal polynomials in dimension $3$, but not beyond