# Tagged Questions

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### Translation of basis for a vector space on the specified distance

In the Euclidean space $XYZ$ is a basis $X_1Y_1Z_1$ defined that is specified by the vectors $\overrightarrow {O_1X_1}$, $\overrightarrow {O_1Y_1}$ and $\overrightarrow {O_1Z_1}$. How to calculate ...
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### Determine whether the following map is a linear transformation.

So I have to determine if the following is a linear transformation: $$T: F(I) \rightarrow F(I)$$ defined by: $$T(f) = 2f$$ I know that if you let $T: V\rightarrow W$ be a linear transformation. Then: ...
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### $\dim(V) = \dim T(V) + \dim T^{-1}(0)$

Let $T\colon V \rightarrow W$ a linear transformation between the real vector spaces $V$ and $W$ both with finite dimension. How can i prove that $\dim(V) = \dim T(V) + \dim T^{-1}(0)$. I can't ...
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### Can someone help ? I have this answer of linear transformation.

Onto? What we have in class that if $n=2$ and $m=3$ that clear $2<3$ ,$T$ will be not onto. He said make three point u have with three variable $=(y,z)$ .then u will have one free variable that ...
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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?