The discussion revolves around the interpretation of a mathematical expression involving rotation matrices and vectors in the context of linear algebra. The original poster seeks clarification on the notation used in their textbook, specifically regarding the meaning of the expression involving angles and vectors.
Participants are actively engaging with the notation and attempting to clarify the meaning behind the expressions. Some guidance has been offered regarding the interpretation of the rotation matrices and the structure of the equation, although there is still some confusion regarding the notation itself.
There is a mention of imposed homework rules that require participants to show some attempt at answering their questions, which has led to discussions about the expectations for posting in the forum.
You still haven't given us all of the context; namely, what Aθ and Aβ represent.Jbreezy said: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 said: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.
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.
Your notation is very confusing.Jbreezy said:Aθ and Aβ are rotation matrices. And what I mean by the βv is that β is sub-scripted before the vector.
Jbreezy said: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.
If you had included something about what you thought the notation meant, I wouldn't have issued the infraction.NOTE: You MUST show that you have attempted to answer your question in order to receive help.
Mark44 said: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.
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.Jbreezy said: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 said: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 - ## 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.Jbreezy said:Yes! That is what I was trying to describe! Does that mean the same thing as ##A_θ(A_βv) = A_{(θ + β)}v##?
Jbreezy said:OK, I will give more indication of what I'm thinking next time. Thank you.