10 What does inner product actually mean? So far most of the cases that I encounter seems to suggest that dot product is the only useful inner product. I mean most of the things that we discuss about …

The dot product is another name for an inner product on $\mathbb {R}^n$ and typically refers to the one you mentioned first. Inner products are more general but share many of the same properties with the …

Feb 12, 2020 · This is an example of an inner product. Of course, not all vector spaces are function spaces, so we need a more general definition that captures the important properties of the "dot …

Mar 18, 2023 · An inner product space is a vector space for which the inner product is defined. The inner product is also known as the 'dot product' for 2D or 3D Euclidean space.

Mar 8, 2020 · 3 Is the inner product simply a definition that conveniently helps to give the notion of the norm and distance between points or vectors in a real vector space? I understand it gives the …

Apr 14, 2012 · The discussion centers around the differences and relationships between the inner product and the dot product, exploring their definitions, applications, and examples in both physical …

So the inner product is designed to work in $\mathbb {C}$ similar to how scalar product works in $\mathbb {R}$. So the question arizes about a geometrical interpretation of an inner product.

Dec 28, 2017 · An inner product is a binary function on a vector space (i.e. it takes two inputs from the vector space) which outputs a scalar, and which satisfies some other axioms (positive definiteness, …

Mar 21, 2018 · The discussion revolves around the necessity of normalizing basis vectors before taking the inner product of a vector represented in different bases, specifically in the context of polar …

Aug 30, 2015 · The inner product on function spaces is exactly the regular dot product, just in infinite dimensions and with a different "weight". Edit, for the issue of orthogonality.