Proof that $\sigma (p(A)) = p(\sigma (A))$ for any polynomial and matrix
54386
What is the relationship between the spectrum of a matrix and its image under a polynomial function?
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
3273
Trouble in proving that $\|x\|_p = \max|x_j|$
28565
Prove $\operatorname{rank}A^TA=\operatorname{rank}A$ for any $A\in M_{m \times n}$
44575
The sigma function (sum of divisors) multiplicative proof
146951
Every countably generated sigma algebra is generated by a random variable
52528
Showing that minimal polynomial has the same irreducible factors as characteristic polynomial
35247
The characteristic and minimal polynomial of a companion matrix
127304
Understanding the algebra of polynomials on a linear space
81327
union of sigma algebra is sigma algebra
132213
Is every real monic polynomial the characteristic polynomial of a real matrix?
144359
A random variable that induces a $\sigma$-algebra the same as the one in the sample space
89553
proof that every finite matrix has an annihilating polynomial
11566
Similar matrices and minimal polynomial
30665
Elegant proofs that similar matrices have the same characteristic polynomial?
133573
characteristic polynomial of the adjacency matrix of a tree
44480
Let $\sigma :\{1,2,3,4,5\} \rightarrow \{1,2,3,4,5\}$ be permutations such that $ \sigma^{-1}(j) \leq \sigma(j)~\forall j, 1 \leq j \leq 5$.