@Vanadium 50
This is not a rhetorical question and is something I’ve been wondering about- Can you (or anyone) please explain what linear algebra technique for solving systems of equations does something we can’t already with the regular elimination method taught in regular algebra? I can do...
@fresh_42
Do you have any examples of "linear approximations to non-linear functions"? That's a new concept for me I think.
Much of what I've seen being done in linear algebra to me doesn't even resemble algebra, which is about solving for unknowns, so I'm not even sure why it's called linear...
I'm pretty much self taught. I didn't study math in college and only started teaching myself afterwards. I got up to calculus and at one point could solve basic derivative and integral problems but am rusty in a bunch of areas. My focus has been LA for the last few months. I'm considering taking...
@Mark44 Your example was helpful, and I didn't mean to imply that it wasn't. Your example was in the context of a different post, though. In this post I am just trying to understand what's unique about linear algebra compared to other areas of math. I used your example here only because it is...
I've been struggling to understand what was the key insight or insights that linear algebra brought to math, or what problems it allowed the solving of that couldn't be solved before. To make a comparison with calculus, I understand that calculus' two key insights were finding a method to...
In the book I'm reading, Before Machine Learning, by Jorge Brasil, I'm on the section that introduces bases for vector spaces. The author gives the example of a vector space with two vectors ##\vec i## and ##\vec j## forming the basis where ##\vec i = (1,0)## and ##\vec j = (0,1)## He then says...
In the bannanas and oranges example, it made me re-think what can qualify as a vector itself. It seems the first vector in the bannas and oranges example consists of 2 coordinates- one is a rule for multiplying bananas, and the other is a rule for multiplying oranges. Can we have a vector where...
With the force example it makes more sense to me I think. Before, I was multiplying two kinds of vectors, but it didn't make sense to multiply those kinds of vectors together. Since I don't have a background in physics, though, I wanted to clarify: Say a rope is pulling a box at an angle. The...
Take a simple example of two vectors A and B where A is a ball travelling and has the coordinates 3,0. Say B is another vector representing another ball traveling and also has coordinate of 3,0. The dot product here is 9, but what does the 9 even mean? Likewise, what would it even mean to say...
I tried to draw an example of a situation where it would be useful to do this. Say you have Alice throwing a ball into the air at an angle of 60 degrees. The ball's path is vector A and has a magnitude of 8. Say Bob is standing at a distance of 12 meters across from Alice and the line between...
@PeroK you showed the two ways of finding the dot product which I have recently learned- i.e. either by multiplying the corresponding units and then adding the products or by multiplying the magnitude of the vectors and then multiplying by the cosine of the angle between them.
I looked up why...
@jedishrfu thanks. I understand visually what we are doing when we add vectors or when we scale vectors because both of these operations can be shown visually on a graph. I do not understand, visually, what it is we are doing when we multiply vectors.