So I had a question which asked me to show that the magnitude of v vector is greater than equal to $0$ with the equality being true if and only if v vector is 0 vector.
The description of the question read "Assuming V is an inner product space, prove..."
I assumed v vector to be $(a_1, a_2, ....., a_n)$, but my professor circled that out and said that I cannot assume $V$ to be $R^n$.
Why is it so?
On
An inner product space is a vector space $V$ over a field $F$ endowed with a product that takes two vectors in $V$ and returns a value in $F$, that satisfies certain properties, called an inner product. A common example is $\mathbb{R}^n$ with the dot product as the inner product, but there are many others. Further reading here : https://en.wikipedia.org/wiki/Inner_product_space#Definition . For your problem you may only assume that the product is an inner product, i.e. that it is a vector space with an additional product on it that satisfies all the properties on an inner product. Hint: the definition of magnitude is the same no matter the inner product.
Because there are many other inner product spaces, $\Bbb C^n$ is an example and even if you assume it is $\Bbb R^n$, what is the inner product? It is not stated what the inner product is so you cannot assume that either.