Definition of applying a polynomial to a linear transformation

Created almost 9 years ago, updated about 8 hours ago

For $p(t)=a_0+a_1t+\cdots+a_kt^k$, define $p(T)=a_0I+a_1T+\cdots+a_kT^k$ for an operator $T:V\to V$. The constant term multiplies the identity operator. Polynomial evaluation respects sums and products of polynomials in the same operator.

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