About the invariance of similar linear operators and their minimal polynomial Notations: F denotes a field V denotes a vector space over F L(V) denotes a vector space whose members are linear operators from V to V itself and its field is F, then L(V) is an algebra where multiplication is composition of functions. τ, σ, φ denote distinct linear operators contained in L(V) m?(x) denotes the minimal polynomial of the linear operator "?" ～ denotes the similarity of the left and right operand, e.g., if τ ～ σ, then τ = φσφ-1 Question: If τ ～ σ are similar linear operators on V, then mτ(x) = mσ(x), i.e., the minimal polynomial is an invariant under similarity of operators. I wonder how it's proved. Thanks for any help!