Let X be an inner product space with complex scalars, and inner product (x, y) &...

 

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Let X be an inner product space with complex scalars, and inner product (x, y) & norm ||x|| = √(x, x). & X = sp{₁} where (₁) Sk a)Prove:{} is linearly independent. N b) Prove: x=(x) \x=X k=1 N c) Prove: x² = 2₁,x)² Vx€ X k=1 Let X be an inner product space with complex scalars, and inner product (x, y) & norm ||x|| = √(x, x). & X = sp{₁} where (₁) Sk a)Prove:{} is linearly independent. N b) Prove: x=(x) \x=X k=1 N c) Prove: x² = 2₁,x)² Vx€ X k=1

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a To prove that the set N is linearly independent we need to show that if there exist scalars c1 c2 dots cn such that c1 N1 c2 N2 dots cn Nn 0 then al... View the full answer