Let (V, ⟨⋅, ⋅⟩) be an inner product space. Prove that the inner product is a continuousfunction

Question

Let (V, ⟨⋅, ⋅⟩) be an inner product space. Prove that the inner product is a continuousfunction
🧐 Not the exact question you are looking for?Go ask a question

Solution 1

To prove that the inner product is a continuous function, we need to show that for any sequences of vectors {x_n} and {y_n} in V that converge to x and y respectively, the sequence of inner products {⟨x_n, y_n⟩} converges to ⟨x, y⟩.

Step 1: Start with the definition of the inner product and its pro Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob

Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solv

This problem has been solved

Similar Questions

Let (V, ⟨⋅, ⋅⟩) be an inner product space. Prove that the inner product is a continuousfunction

7. Let (V, ⟨⋅, ⋅⟩) be an inner product space and let R, S be subsets of V .(a) Prove that S ∩ S⊥ = 0

Let v be a vector and let k be a scalar. From the axioms of a vector space, prove that if kv = 0 theneither k = 0 or v = 0.

8. Let (X, d) be a metric space and let S ⊆ X. Prove that dS (x) = 0 if and only if x ∈ S

Prove that if W is a subspace of a finite dimensional vector space V, then dim(W) ≤ dim(V).

1/3