difference between dot product and inner product?

Question

I was wondering if a dot product is technically a term used when discussing the product of $2$ vectors is equal to $0$. And would anyone agree that an inner product is a term used when discussing the integral of the product of $2$ functions is equal to $0$? Or is there no difference at all between a dot product and an inner product?

Answer 1

When it comes to vectors, the dot product and inner product are the same thing. The term "inner product" also applies to orthogonal functions, which are analogous to orthogonal vectors. Namely, if the inner product of two functions is equal to zero, while the inner product of each function with itself is nonzero, then the two functions are orthogonal. The inner product of functions depends on an interval and weighting factor that are associated with the definition of orthogonality.