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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