# variable unit vectors?

• September 15th, 2020, 07:43 PM
Aaedimus
variable unit vectors?
Hey! Just getting into linear algebra and Calc 3, and we're looking allot at unit vectors etc, but the vectors i,j,k etc or w (cross product of u and v) generally still use 1 as their base unit and scale linearly. Last week we got into linear transformations, and it got me thinking.... If a unit vector represented a scaling nonlinear formula that would do all kinds of crazy things! The most obvious example I could think of that reminded me of this was I imagine if the unit vector represented something like a 1/inf at zero and scaled out, you'd almost have something representing spacetime fabric near black holes.

What other way though are nonlinear unit vectors used in real life applications though? It seems like such an interesting concept.
• September 15th, 2020, 10:07 PM
mathman
Quote:

Originally Posted by Aaedimus
Hey!The most obvious example I could think of that reminded me of this was I imagine if the unit vector represented something like a 1/inf at zero and scaled out, you'd almost have something representing spacetime fabric near black holes.

Don't mix mathematical concepts with physics.
• September 16th, 2020, 05:56 AM
geordief
Quote:

Originally Posted by mathman
Quote:

Originally Posted by Aaedimus
Hey!The most obvious example I could think of that reminded me of this was I imagine if the unit vector represented something like a 1/inf at zero and scaled out, you'd almost have something representing spacetime fabric near black holes.

Don't mix mathematical concepts with physics.

I am not a physicist or a mathematician but didn't Einstein get help from hid mathematics friends to find mathematical tools to apply to the physical ideas he had?

If there is an area of maths that has already been developed does it not sometimes find its application as a new area of physics presents new problems?
• September 19th, 2020, 08:36 AM
Bufofrog
Quote:

Originally Posted by Aaedimus
If a unit vector represented a scaling nonlinear formula

What do you mean by this?

Quote:

unit vector represented something like a 1/inf
How could a unit vector, which by definition is 1 also be equal to 1/inf?
• September 19th, 2020, 09:23 AM
geordief
Quote:

Originally Posted by Bufofrog
Quote:

Originally Posted by Aaedimus
If a unit vector represented a scaling nonlinear formula

What do you mean by this?

Quote:

unit vector represented something like a 1/inf
How could a unit vector, which by definition is 1 also be equal to 1/inf?

I thought he might mean that ,as the vector increased linearly it would represent a non linear progression.

Is he trying to start his vector basis in a region that is undefined ?

Like you ,I don't see how the unit vector (the basis vector,I imagine) could represent a zero quantity unless 1/infinity was perhaps taken as as "almost" limit (whatever that might mean ;nothing at all mathematically I would say)

It would probably be great if we could introduce mathematical tools into areas of physics (singularities) that we don't understand . Not being a mathematician or a physicist I have no idea if this sort of an approach could be used.