# Tagged Questions

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### Constructing regular integer matrices with distinct integer eigenvalues

How can I construct matrices with positive integer values and distinct integer eigenvalues (not necessarily positive, but 0 should not be an eigenvalue). The standard-method to construct matrices ...
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### Do T and T* have the same eigenvalues with the same algebraic multiplicity?

I know that the eigenvalues of T* are the conjugates of T's eigenvalues , but how can I see each eigenvalue of T and it's conjugate , the eigenvalue of T*, have the same algebraic multiplicity?
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### find the vector $(x,y,z) \in \mathbb{R}^3$ and the constants $\lambda \in \mathbb{R}$ such that $T(x,y,z) = (\lambda x, \lambda y, \lambda z )$

Let $T : \mathbb{R}^3 \rightarrow \mathbb{R}^3$ defined by : $$T(x,y,z) = (x-y+4z,3x+2y-z,2x+y-z)$$ How can i find the vector $(x,y,z) \in \mathbb{R}^3$ and the constants $\lambda \in \mathbb{R}$ ...
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### Linear transformations and eigenvalues [duplicate]

Let $T: \mathbb C^n \rightarrow \mathbb C^n$ be linear. Let $\beta$ and $\gamma$ be any two ordered bases. Prove that the eigenvalues of $[T]_\beta$ and $[T]_\gamma$ are the same. Can anyone provide ...