Suppose TEL(V) and v € V. (a) (b) Prove that there exists a unique monic polynomial p of smallest degree such that p(T)v = 0. Prove that p divides the minimal polynomial of T.
Suppose TEL(V) and v € V. (a) (b) Prove that there exists a unique monic polynomial p of smallest degree such that p(T)v = 0. Prove that p divides the minimal polynomial of T.
Suppose TEL(V) and v € V. (a) (b) Prove that there exists a unique monic polynomial p of smallest degree such that p(T)v = 0. Prove that p divides the minimal polynomial of T.
The problem is from Linear Algebra Done Right by Axler. Could you teach me how to do this in detail?
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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