Recent content by NoahsArk

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...

I meant some kind of word problem example using a specific real world application to illustrate how the dot product works.

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...

@Steve4Physics are there any more mundane examples of how dot product multiplication works that you can think of which don't involve forces?

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.

I'm confused about what we are really measuring when taking the dot product of two vectors. When we say we are measure "how much one vector points in the direction of the other", that description is not clear. At first I thought it meant how much of a shadow one vector casts on another and I...

Thanks @fresh_42 and @PeroK. @fresh_42 yes I see I had the slope coordinates backward for m =2/3 @PeroK I did confirm with a few examples, plugging in x and y and x0, y0 with different numbers, that the third line form you wrote above, the vector form, works. I was just observing what’s...

@PeroK "I'll leave it to you to check that if we take the set of points ## (x,y) ## where ## (x,y) = (x_0, y_0) + t(1,m) ## then these points satisfy the equation ## y - y_0 = mx (x-x_0) ## " I think I am starting to understand this, and, if I am, then this means that whereas ## y = mx + b ##...

Thanks Fresh. Sorry I should've indicated beginner level instead of intermediate for my question since I am just starting to learn linear algebra. I was not able to follow all the equations you wrote.

Thanks. I just started studying linear algebra, so I am not sure what (1,m) means. I thought direction of a vector was measured by an angle. Can you please give an example where: I am also a bit unclear on what the t means- my understanding is that it's a factor that you can use to scale up or...

I am having trouble with the concept that the equation L = {x + tv} is the more general form of the more familiar y = mx + b (In the first equation there should be a vector sign above the x and the v). It's hard for me to see the similarities between these two equations. 1: Even if we are...