# Effect of Basis on Linear Transformation Matrix

Algebra Level 4

Let $$T: V \to V$$ be a linear transformation in a finite-dimensional of a vector space. Then, for some choice of basis $$\mathcal{B}$$ and matrix $$M_\mathcal{B}$$, $$T(v) = M_\mathcal{B}v$$. Which properties of the matrix $$M_\mathcal{B}$$ remain unchanged regardless of basis $$\mathcal{B}$$?

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