Inner Product Spaces (𝑉,𝐹,⟨·,·⟩)

• is a type of mathematical space
• an inner product (⟨·,·⟩) induces a norm (||·||_⟨·,·⟩) defined as: ||·||_⟨·,·⟩ = √⟨·,·⟩

  • thus all inner product spaces (𝑉,𝐹,⟨·,·⟩) are also normed vector spaces (𝑉,𝐹,||·||_⟨·,·⟩)

Inner Product Spaces - Examples

• Every finite inner product space is a Hilbert space (𝓗)

Resources

• see page 367 of Linear Algebra and its Application 4th edition ~ David C. Lay