Does this just mean...matrices?

[Jbreezy]

Does this just mean...matrices

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Office_Shredder]

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?

 

[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.

 

[Mark44]

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.

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

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

Please clarify what all of the symbols in your equation represent.

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

 

[Jbreezy]

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

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

Please clarify what all of the symbols in your equation represent.

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

A_θ and A_β 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.

 

[Mark44]

A_θ and A_β are rotation matrices. And what I mean by the βv is that β is sub-scripted before the vector.

Your notation is very confusing.
$A_θ(A_βv) = A_θ + βv$

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.

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.

From the PF rules:

NOTE: You MUST show that you have attempted to answer your question in order to receive help.

If you had included something about what you thought the notation meant, I wouldn't have issued the infraction.

 

[Jbreezy]

Your notation is very confusing.
$A_θ(A_βv) = A_θ + βv$

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.

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.

 

[Mark44]

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".

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.

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.

 

[Jbreezy]

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.

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.

 

[Mark44]

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

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.

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