linear algebra proofthanks Let V be a finite-dimensional inner product space over C (resp. R). LetTEL(V) be normal (resp. self-adjoint). Let ur(x) = P(F) be the monic polynomialof smallest degree such that pr(T) = 0. (Existence and uniqueness of pr(x) followsfrom homework 3, problem 10; ur(x) is called the minimal polynomial of T.)Prove thatµT(x) = (x − λ₁) ··· (x - Am),where A₁,..., Am are the distinct eigenvalues of T.

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Answered: Let V be a finite-dimensional inner…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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linear algebra proof

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Let V be a finite-dimensional inner product space over C (resp. R). Let
TEL(V) be normal (resp. self-adjoint). Let ur(x) = P(F) be the monic polynomial
of smallest degree such that pr(T) = 0. (Existence and uniqueness of pr(x) follows
from homework 3, problem 10; ur(x) is called the minimal polynomial of T.)
Prove that
µT(x) = (x − λ₁) ··· (x - Am),
where A₁,..., Am are the distinct eigenvalues of T.

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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