Well what you say would make more sense if I were learning direct product before anything else, which I'm not. But in any case just because material has an underlying sequence to it doesn't necessitate having it be learned in a particular conceptual order. And I'm not even asking to know...
I think everyone can only actually learn by understanding how things are related - clearly inner product, dot product and direct product are related. But beyond this there is a wide variation between individuals in the way this is done.
However it is true that apparently to understand the...
It was mentioned in a discussion about tensors, and tensors are a generalization of vectors - just sets of numbers subject to the same linearity rules as vectors. A direct product is also known as a tensor product - doesn't the direct product have any meaning in linear algebra? Or can it not...
ok well I pretty much new the essentials of what has been mentioned already, it just seems strange to me that once you arrive at this scalar value that comes from the space it doesn't actually have a position in space. It's not hard to imagine it's possible, it just seems like a strange thing to...
I'm just trying to understand from a linear algebra standpoint how they define dot product from the inner product and how this gives rise to a definition of length and angle. somehow there is a way to combine points in space to a scalar value that unambiguously determines length and angle? Is...
When I say sum I'm just referring to the "+" sign after the arrow. And yeah I understand the meaning of the partial derivative for the most part... I think. My lack of confidence doesn't come from this at least. Here is a more detailed depiction of what step I'm talking about...
Thanks that helped a lot, it's just weird how one can apply as you just did "as far as F is concerned". I have trouble understanding why this is ok to do just because it seems like by treating them as independent one is making a false statement. It makes sense that F can't really tell them apart...
I understand the chain rule for the most part, and I understand why normally there would be a sum - it makes sense when the two variables are independent - but now I have a Y and a Y', and I'm not convinced of why they are treated independently so that the same rules apply. I thought I made this...
1. This is really more of a math question than a physics one... it's in calculus of variations while deriving a proof for the Euler equation. I always hit a mental road block when it goes from this step:
2. F(x,Y,Y') = I(e) --> \frac{dI}{de} = \frac{\partial F}{\partial Y} \frac{dY}{de} +...