Vector notation

This article may be confusing or unclear to readers. In particular, the article uses many terms which are nowhere defined in Wikipedia, and are not commonly defined in modern mathematics: rectangular vector, spherical vectors, etc. Moreover, except for the lead, it is not about notation, but about the representation of vectors (or points?) by means of coordinates.. Please help clarify the article. There might be a discussion about this on the talk page. (January 2024) (Learn how and when to remove this message)

Vector notation

Vector arrow
Pointing from A to B

Vector components
Describing an arrow vector v by its coordinates x and y yields an isomorphism of vector spaces.

Scalar product
Two equal-length sequences of coordinate vectors and returns a single number

Vector product
The cross-product in respect to a right-handed coordinate system

In mathematics and physics, vector notation is a commonly used notation for representing vectors,^[1][2] which may be Euclidean vectors, or more generally, members of a vector space.

For representing a vector, the common typographic convention is lower case, upright boldface type, as in v. The International Organization for Standardization (ISO) recommends either bold italic serif, as in v, or non-bold italic serif accented by a right arrow, as in ${\displaystyle {\vec {v}}}$.^[3]

In advanced mathematics, vectors are often represented in a simple italic type, like any variable.^{[citation needed]}