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Vector notation - form versus vector?

• Context: Undergrad
• Thread starter Thread starter MrNeu
• Start date Start date Oct 10, 2013
• Tags Tags Form Notation Vector Vector notation

Click For Summary

Discussion Overview

The discussion revolves around the notation used for vectors, specifically the differences between various representations such as arrows, underlining, and boldface. Participants explore the significance of these notations and their implications in mathematical contexts, including the distinction between vectors and tensors.

Discussion Character

• Exploratory
• Technical explanation
• Debate/contested

Main Points Raised

• Some participants note that there is no standardized way to represent vectors, with different conventions used by different individuals.
• One participant mentions that underlining might be confused with emphasis, and expresses skepticism about its common use for vectors.
• Another participant discusses the abstract definition of vectors, emphasizing that the concept does not inherently include direction and magnitude, which are characteristics of normed vector spaces.
• Several participants list various notational forms for vectors, including \(\vec{v}\), \(\mathbf{v}\), and others, highlighting the diversity in representation.
• One participant questions the aesthetic choice of underlining for vectors, suggesting that other notations are preferable.

Areas of Agreement / Disagreement

Participants generally agree that multiple conventions exist for vector notation, but there is no consensus on the best or most appropriate method. The discussion remains unresolved regarding the significance of these notational differences.

Contextual Notes

Some limitations include the lack of clarity on the implications of different notations in various mathematical contexts and the absence of a definitive standard for vector representation.

MrNeu Messages 4 Reaction score 0 Hi there, During a recent tutorial, I asked my tutor about the notation he uses for vectors - he draws the little half arrow above them and I was curious whether that was significant, as opposed to just underlining vectors. He said it was a mathematical technicality and suggested I look up "forms versus vectors" on Google. However, I haven't been able to find anything conclusive. Could anyone explain the difference between forms and vectors, and the difference in notation? Thanks! Physics news on Phys.org

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jedishrfu Mentor Insights Author Messages 15,636 Reaction score 10,435 Some info on vector notation: http://en.wikipedia.org/wiki/Vector_notation D H Staff Emeritus Science Advisor Homework Helper Insights Author Messages 15,524 Reaction score 768 It's just his convention. Other people have other conventions. There is no standardized way to represent vectors. In print you'll often see vectors as bold upright font, scalars as a plain italic font: ##\mathbf{v}## versus ##v##. Given the shortage of bold upright pieces of chalk (or magic marker), people have to use some other convention when writing on the chalkboard or whiteboard. That's when you'll see stuff like ##\vec v##, or ##\tilde v##, or whatever. Since there is no standard convention, you'll just have to live with the fact that different people use different conventions. SteamKing Staff Emeritus Science Advisor Homework Helper Messages 12,828 Reaction score 1,673 Underlining to indicate vectors might get confused with underlining for emphasis. I don't recall seeing this notation used very often (if at all). D H Staff Emeritus Science Advisor Homework Helper Insights Author Messages 15,524 Reaction score 768 Part of what the instructor is getting at is (I think) the difference between a vector and a tensor. In the most abstract, a vector is a member of a vector space. The rules are pretty simple: Vectors can be added associatively and commutatively, there's a zero vector, vectors have additive inverses, and vectors can be multiplied by a scalar. Not one word about how they transform (that concept is key to one-forms, and to tensors in general). There's not even one word in that abstract concept of vectors and vector spaces about vectors being something with a direction and a magnitude. So even the notation ##\vec v## is a bit misleading for vectors. Some but not all vectors can be characterized as having a direction and a magnitude. That concept pertains to normed vector spaces, but not to vector spaces in general. pasmith Science Advisor Homework Helper Messages 3,346 Reaction score 1,890 I've only ever seen \mathbf{v} or \vec v or \underline{v} (which is only ever used in manuscript, and is an instance of a general convention that what is underlined in manuscript should be in boldface when typeset) used for members of \mathbb{R}^n and on occasion \mathbb{C}^n (or used for functions whose codomains are \mathbb{R}^n or \mathbb{C}^n), both of which are equipped with "standard" operations, bases, inner products and norms. For any other vector space - such as the space of functions from an arbitrary non-empty set to \mathbb{R} under pointwise addition and scalar multiplication - no special font or symbol is used. In the other direction, I've seen plenty of texts which don't use special fonts or symbols for vectors. Mark44 Mentor Insights Author Messages 38,090 Reaction score 10,640

SteamKing said: Underlining to indicate vectors might get confused with underlining for emphasis. I don't recall seeing this notation used very often (if at all).

The only place I've seen underlining used for vectors is here. If someone goes to the effort of writing LaTeX code to underline a vector, I wonder why they didn't use the arrow above notation, as in ##\vec{v}##. The underline business for a vector just seems ugly to me. D H Staff Emeritus Science Advisor Homework Helper Insights Author Messages 15,524 Reaction score 768 There are so many ways to represent that something is a vector: \vec{v} \quad<br /> \overset{\rightharpoonup}{v} \quad<br /> \tilde{v} \quad<br /> \bar{v} \quad<br /> \underline{v} \quad<br /> \mathbf{v} \quad<br /> {\frak{v}} \quad<br /> \text{and of course} \quad<br /> v<br /> Mark44 Mentor Insights Author Messages 38,090 Reaction score 10,640

D H said: There are so many ways to represent that something is a vector: \vec{v} \quad<br /> \overset{\rightharpoonup}{v} \quad<br /> \tilde{v} \quad<br /> \bar{v} \quad<br /> \underline{v} \quad<br /> \mathbf{v} \quad<br /> {\frak{v}} \quad<br /> \text{and of course} \quad<br /> v<br />

You're just showing off jedishrfu Mentor Insights Author Messages 15,636 Reaction score 10,435

Mark44 said: You're just showing off

You floks forgot one: The R vector...

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