# Homework Help: Does this just mean .matrices

1. Aug 26, 2013

### Jbreezy

Does this just mean.....matrices

1. The problem statement, all variables and given/known data

What does this mean $βv$ but pretend that the angle beta is lower case. This is how my book wrote it.

2. Relevant equations

3. The attempt at a solution

2. Aug 26, 2013

### Office_Shredder

Staff Emeritus
It's common for vectors to be denoted with bold font and scalars with greek letters, so that's what I would guess, but all that really is is a guess without any context. Can you post the sentence or paragraph where v and beta appear?

3. Aug 26, 2013

### Jbreezy

Yep I can.
Use matrix vector products to show that for any angles theta and beta and any vector v in $R^2$ , $A_θ(A_βv) = A_θ + βv$
Remember that β is lower case on the right side of the equation. I don't know how to make it that way. But read βv as lowercase β.

4. Aug 26, 2013

### Staff: Mentor

You still haven't given us all of the context; namely, what Aθ and Aβ represent.

If I had to take a guess, Aθ and Aβ are matrices of some kind, but that assumption isn't consistent with what you have on the right side of the equation: Aθ + βv. Since v is a vector in R2, then βv is, as well, so Aθ must also be a vector in R2. Otherwise the addition is not defined.

BTW, β is the lower case form of the Greek letter beta. Upper case beta is B.

5. Aug 26, 2013

### Jbreezy

Aθ and Aβ are rotation matrices. And what I mean by the βv is that β is sub-scripted before the vector. Why do you give me a warning? My question is one about notation not about actual doing a problem so really there is nothing for me to try. I'm not looking for a solution in the typical sense I just want to know what something means.

6. Aug 26, 2013

### Staff: Mentor

$A_θ(A_βv) = A_θ + βv$

What I think you mean is this:
$A_θ(A_βv) = A_{(θ + β)}v$
The meaning here is that rotating a vector v through an angle β, and then rotating that vector through and angle θ is the same as rotating v through an angle θ + β.

The notation as you wrote it makes no sense. The right side is the sum of a vector in R2. The right side is the sum of a 2 X 2 matrix and a vector in R2. This addition is not defined.
From the PF rules:
If you had included something about what you thought the notation meant, I wouldn't have issued the infraction.

7. Aug 26, 2013

### Jbreezy

Mark, I agree with what you wrote "$A_θ(A_βv) = A_{(θ + β)}v$" because this is what I ended up with. I want to also mention that it is not my notation. It is the books notation. I have never seen something written this way. I did not think that I would have to say what I think the notation meant. I think that is a little strict. I understand the rules but it is just a notation question. Do what you want though. Thanks for the help.

8. Aug 26, 2013

### Staff: Mentor

Did it look like this?
$A_θ(A_βv) = A_{θ + β}v$

On the right side β is a subscript, and maybe that's what you meant when you said "lowercase".
The rules are what they are, but it's not expected that you will answer any question you post - just give some indication that you have given the question some thought.

In any case, I will rescind the infraction this time.

9. Aug 26, 2013

### Jbreezy

Yes! That is what I was trying to describe! Does that mean the same thing as $A_θ(A_βv) = A_{(θ + β)}v$???

OK, I will give more indication of what I'm thinking next time. Thank you.

10. Aug 26, 2013

### Staff: Mentor

Yes - $A_{(θ + β)}v$ means the same thing as $A_{θ + β}v$; namely, the matrix of a rotation through and angle of θ + β.