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Suppose u = (u1,u2) and v = (v1, v2) are two vectors in R2. Explain why...

Suppose u = (u1,u2) and v = (v1, v2) are two vectors in R2. Explain why the operations (u * v) = u1v2 cannot be an inner product.

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Answer #1

If v is an inner product space and by property of negativity says ,

for all .

Now , is given by where

Take then ,

But .

So this operation violates non-negativity property and hence cannot be an inner product .

.

.

.

If you have any doubt please comment .

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