Linear Algebra 2h: What Else Works like Geometric Vectors?

[douglasespindola]

In economics, I guess vectors can be interpreted as, let's say, a picture of a determinated state of things. For example, it can be an observation of an individual with it's preferences, income, wealth, age, years of education, etc. Thus, accelerations and velocities can be interpreted as it's respective changes of these variables. Thank you for your wonderful classes, Pavel!

[cometmace]

I think it *is* very intuitive that forces should add like geometric vectors.  Both are direction and magnitude tuples.

[faisalsal]

Scalar Operation on a "Vector", outputs a new "Vector"
"Displacement" is a vector and multiplying it by 1/T (Time - which is a Scalar) result in a new Vector "Velocity".
As "Velocity" is a vector then multiplying it by 1/T (Time - which again is a Scalar) result in a new Vector "Acceleration".
As "Acceleration" is a vector then multiplying it by M (Mass - which is a Scalar) result in a new Vector "Force".

Scalar Operation on Vector "Displacement" --> Vector "Velocity"
Scalar Operation on "Vector Velocity" --> Vector "Accelaration"
Scalar Operation on Vector "Acceleration" == ??

[curtpiazza]

It's all beginning to make sense! 😊

[antonellomascarello]

0:43 : Displacement
4:37 : velocities
9:30 : Acceleration
10:41 : Forces

[schokolademan]

When accelerations add by the parallelogram rule than forces are added by the parallelogram rule because forces are just multiplying with m, distribution rule

[somekid]

Wait, isn't there a matrix that gives you the derivative of any polynomial? Which would mean you can treat derivatives like vectors, and be a really elegant explanation, and honestly I'm pretty sure a lot of contemporary mathematicians would've recognized this once they saw those matrices; they were all famous for a reason, you know.

[isreasontaboo]

I'm not sure what's so special about postulating that forces can add up according to regular vector rules if you define it with an equality that does multiply a scalar and another vector, just like you divided the distance and velocity by a time scalar too.

[budokan]

Forces add up because according to F=ma they are linear combinations of accelerations. They add up because the accellarations add up. Think m's as scalars that we multiply with accelerations...

[Hythloday]

Forces work like vectors because:
Conservation of Information --->
Symmetry Conservation Laws (Emmy Noether)
E.g. Translation Conservation of Momentum
? ? ? ? ? ? ? ?

[MrCrazyShock]

To demonstrate that Velocity is a vector you say: Let's divide the Displacement, which is a vector, by Time, which is a constant. Knowing that a vector divided by a constant remains a vector, we demonstrate that Velocity is also a vector.

So why not use the same logic to the Force. The Acceleration is a vector, and the Mass is a constant. So dividing the Acceleration by the Mass will necessary produce another vector, which is the Force.

Is this making sense?

[jaysmith]

Is there any sense in which the cross product generalizes to linear algebra, or is it just some goofy thing that is only defined for 3-D space?

[rkpetry]

60 in./hr. Is awfully slow for a ladybug... 60 ft./hr. (5 sec./in.) would seem more realistic... meanwhile thanks, for the math talk...