You are Here: Home >< Maths

Help on dot and wedge symbols watch

1. I'm reading a paper where the symbols are throwing me off.

For the 'dot' symbol, I see which makes sense, but also appears. I realize the dot product is commutative, but
1) Why change the order?
2) is given as an initial condition, yet shows up in the second initial condition. If the operation is in fact commutative, then why place in the second condition when it would just zero out the term.

Note - I doubt this is indicative of normal matrix multiplication since is seen.

Does anyone know of another meaning for when talking vectors?

For the symbol, I've seen and the only thing I've stumbled across is the exterior product. Does anyone know of other possibilities or am I on the right track with the exterior product?
2. You know that is a differential operator, right? Which means that , just as .

In this context, is almost certainly the same as ; it's just the vector cross product. (In 3-space, this is basically also the same as the exterior wedge product, but you probably don't want to think of it like that).
3. (Original post by DFranklin)

1) You know that is a differential operator, right? Which means that , just as .

2) In this context, is almost certainly the same as ; it's just the vector cross product. (In 3-space, this is basically also the same as the exterior wedge product, but you probably don't want to think of it like that).
1) I know that the first is just the divergence, and I'm aware of the faulty notation since it 'views' as a dot product but no true product is taking place. Rather, the operators are acting on each component of the vector, respectively. I'm still lost on the meaning of

I'm working in 3D, so could it be that I multiply the matrices as normal but the dot is to let me know that I allow the operators to act on the entries rather than true multiplication. Meaning would give me a matrix but would give me a matrix? That's all I've been able to come up with so far.

2) I googled 'cross product' with the suggestion, and I didn't realize the wedge is used in physics notation. I'm good on this one now. Thanks.
4. Be careful with though - if it's the exterior product, then it means . But in , it's probably just the normal cross product, because the exterior product would give zero.

The operation of taking two vectors and forming a matrix is called the outer product (not to be confused with the exterior product), usually denoted ; I really don't think it would be appropriate to denote it by the same symbol as the inner product. Now I'm just guessing, but I think is .
5. (Original post by monty1618)
1) I know that the first is just the divergence, and I'm aware of the faulty notation since it 'views' as a dot product but no true product is taking place. Rather, the operators are acting on each component of the vector, respectively. I'm still lost on the meaning of

I'm working in 3D, so could it be that I multiply the matrices as normal but the dot is to let me know that I allow the operators to act on the entries rather than true multiplication. Meaning would give me a matrix but would give me a matrix? That's all I've been able to come up with so far.

2) I googled 'cross product' with the suggestion, and I didn't realize the wedge is used in physics notation. I'm good on this one now. Thanks.
Well, , whereas . The vital point is that does two things - it acts as a vector, and it acts as a differential operator. It differentiates u if u comes to the right of it, but not to the left - notice that is a perfectly legitimate expression, but is still an operator. You'd only ever see or similar, of which the meaning should be obvious.

Also note that operates on a vector. but operates on a scalar.
6. I've seen some good ideas so far, but I haven't given enough info to rule out certain things.

is an expression from the paper.

must be able to act on a vector, and the result must be of the same dimensions as , being . So must be either a scalar or a matrix.
7. (Original post by Zhen Lin)
The operation of taking two vectors and forming a matrix is called the outer product (not to be confused with the exterior product), usually denoted ; I really don't think it would be appropriate to denote it by the same symbol as the inner product. Now I'm just guessing, but I think is .
I haven't ran it yet, but I think that comes out the same way as treating as a matrix, even though your way is quicker by far.

So basically, treat it as a dot product as usual, but it will just remain an operator until applied to another vector is what I'm getting from it.
8. (Original post by generalebriety)
Also note that operates on a vector. but operates on a scalar.
I'm almost completely sold on treating it as the normal dot product if can act on a vector. Wouldn't it be ok to just apply to each component of a vector or would that present a problem?
9. Ok. I have it now, so disregard the last question(s). And Franklin, you had it pegged from the start, but for some reason the non-commutativity wasn't registering.

Anyway, thanks to you all.
10. (Original post by monty1618)
I'm almost completely sold on treating it as the normal dot product if can act on a vector. Wouldn't it be ok to just apply to each component of a vector or would that present a problem?
Oh, yes, that'd be fine too. Good point.

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: August 26, 2008
Today on TSR

University open days

• Southampton Solent University
Sun, 18 Nov '18
Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
Poll
Useful resources

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

How to use LaTex

Writing equations the easy way

Study habits of A* students

Top tips from students who have already aced their exams

Chat with other maths applicants