And that's because when the basis vectors change, the components adjust in a complementary way to keep the vector the same. The vector itself is independent of which coordinate system you use. And the same is true for tensors, only now instead of having just two components, a general tensor can have any number of them
So one is north, south, east, and west. So that's the absolute coordinate system , and you could say hey, I'll meet you on the north side of the house. And if we both know the coordinate system , we can both meet on the north side of the house.
So that's the absolute coordinate system , and you could say hey, I'll meet you on the north side of the house. And if we both know the coordinate system , we can both meet on the north side of the house. There's an ego-centered coordinate system with its front, back, left, right.
And if we both know the coordinate system , we can both meet on the north side of the house. There's an ego-centered coordinate system with its front, back, left, right. And you can attach that to a house and say, I'll meet you in front of the house.
And people have a sense of what the front of the house is. There's also a relative coordinate system . So this is where you could draw yourself a line between myself and the books, and I could say I'll meet you
And then you'd have to have a different rule for every room. So this is a spatial coordinate system which helps us, gives us new tools for thinking and doing things. Driving on the left would be impossible in populations that only have absolute coordinate systems-- north, south, east, and west.
For example, this vector can be written as 3x hat plus 2y hat. But I can also write this using a different coordinate system . And with these new basis vectors, the original vector is now written as 2a plus 1b.
of in the space out here and there are different coordinate systems um that are operating within this pathway so uh the two most basic coordinate systems that the brain uses are a coordinate system centered essentially on the person's head um a self-centered coordinate system and then an external coordinate
operating within this pathway so uh the two most basic coordinate systems that the brain uses are a coordinate system centered essentially on the person's head um a self-centered coordinate system and then an external coordinate system ref reference to some other uh geographical landmark and part of the operations here is essentially keeping
in the form of a matrix. And just like with vectors, you can change a tensor from one coordinate system to another, and the tensor stays the same. So that's why Einstein had to use them to build his new theory.
So I described for a single aircraft you may have, say, discretes, discontinuous, you may have even safety reports that are associated with that flight. How do you put all those on-- you can't imagine putting those on the same coordinate system and doing, let's say, clustering and checking for anomalies. So what we do is here is have a separate kernel function for each modality.
systems to make the flight. The first one is of course an Earth-centered system so when we're in Earth orbit, the center of the Earth is the center of the system. It's an orthogonal system, XYZ coordinates, standard old orthogonal coordinate system . When we started on our way to the Moon we switched to a sun-centered system. Same thing XYZ coordinates, but it was a sun-centered system because the Earth and the Moon and us, we're all in that solar system. And then as we got closer to the Moon, we switched over to a lunar-centered system.
This is not very realistic. But in principle, Pythagoras' theorem gives you a formula for calculating the distance along a straight line in some coordinate system . So you have coordinates x and y.