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3 questions
2
votes
2
answers
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Find characteristic polynomial of $A^2+I$.
Let $A$ be a $3\times3$ matrix with $A^3+A+I_3=0$ with coefficients in
$\mathbb{Q}$. Find the rational canonical form of $A$ and the
characteristic polynomial of $A^2+I_3$.
Let $p(x)=x^3+x+1$. Since $...
- 163
2
votes
0
answers
201
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Given a 4x4 Singular Matrix. find characteristic polynomial
I'm trying to solve this issue:
Given A, a 4x4 singular Matrix. It is known that $\rho(A+2I)=2$ and $|A-2I| =0$.
Find the characteristic polynomial of A, is A similar to a diagonal matrix?
I've ...
- 411
21
votes
1
answer
983
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What do characteristic polynomials characterize?
Let $R$ be an integral domain and $F$ a finitely generated free module over $R$. For a linear transformation $\alpha\in\operatorname{End}_R(F)$, the characteristic polynomial is \begin{equation}
p_\...
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