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
And I think in terms of the homogeneity or the heterogeneity of people in a neighborhood, I'd maybe think about two vectors . One vector is, typically speaking, suburban neighborhoods tend to be more homogenous than urban neighborhoods. Homogenous neighborhoods tend to be in places that have similar characteristics, whether it's proximity to running trails, or proximity to great public schools, or proximity to
And once you map words into a vectorial form, you can understand the machine. The vector actually encodes some semantic meaning of the word itself. And then it can discover certain relationships.
place B perhaps you had stored memory that there was food there u then the system should be able to generate this this vector AB and that send that to the motor system and drive the system uh in the in the right direction. However, if this path is blocked, then the system should equally well be able to generate any set of vectors which would get you
And only a fraction of it is about science. So vector control, controlling mosquito-borne diseases, actually is more than malaria.
I'd talk about democratizing learning and how this Citizen Schools idea was one of the top 10 ideas 100 years from now that'll kind of change the vector of society. And I would talk to people who invented the personal computer, or Sergey and Larry.
Extension of this approach, if we succeed, it can be used in many diseases. Especially vector born diseases. Here we call them NTD's or neglected tropical diseases.
- Let's think about a really simple vector , say 1 in the x-direction and 2 in the y-direction. If I reflect this vector along the line y equals x and then reflect it about the x-axis, I get this. But if I start again and instead reflect it first about the x-axis and then along y equals x, I get this, which is totally different.
A simple kind of tensor is a vector . You can write a vector as a set of components multiplied by their basis vectors . For example, this vector can be written as 3x hat plus 2y hat.
As the particle wave follows a path, its phase increases. Winding the vector around. So now the big question is how much does the phase change for each path?
of the goods. Okay, J with a circle for outside option. So if you look at the value function on the inside option, they're choosing the vector of intermediate inputs to use the vector of factors. They're maximizing profits, but they're perceiving some wedges. They're perceiving wedges that they have accepted from the
So that's really, I don't think it. The other vector in that soup has been working on the Iranian-American diaspora
The urban is where we see more diversity on a neighbor-by-neighbor basis, right? But the other vector is you also have the circle of life going on in all these neighborhoods. So in every single neighborhood, you have people who've been there for 20 or 30 years and are getting older, and then you have people who've moved in, and then
We've been able to survive every financial downturn and sometimes the Engine's been funding the business because we didn't have a game. And then there were vector graphics with little wire frames moving around and things.
You wrote down some axioms, and then you proved some theorems. a little vector sign over it.
You wrote down some axioms, and then you proved some theorems. So a single vector in spacetime is written p mu.
Today, I think women have a large number of role models and examples of how successful women can be. So in a viral vector platform, what they do is that they take a harmless virus, like an adenovirus, which is like the common cold virus.
Look at this. That individual had a gun put on him. He redirected the vector . He actually did some good stuff.
And if the vector of any object in motion intersects with the car, and the driver is not braking it, they will break it.
The delivery vector that Spider Man uses to fire off his goop lacks a little finesse.
it transforms from a vector into a dead end for human disease the other thing that's great
If there's a vector and there's an angle, probably some scientist is interested in it.
And what this vector field shows you, what all the arrows show you, is the effect that a stationary student has on a moving student.
And support vector machines, or kernel machines, for short, solve both of these problems.
The down vector is local everywhere you are in an irregular object.
Matrix multiplication is like vector multiplication.
Twice a year with a tablet-- you take six to seven years. But with the vector control, you probably bring it down to three years. Or two years to control transmission.
The red vector that's following the mouse?
incredibly clear vector that just pointed back to this one location in New Jersey.
your velocity vector . But if you don't change your velocity vector , you're going in that direction and there's nothing you can do about it. And you can roll you can do anything you
up into one master Vector diagram of what I'm saying about China you'll find difficulty because it is uh it's like
looking kind of vector -based animations you could create these really pristine uh high resolution still images but you
And while adding up vectors is hard, adding scalars is a piece of cake.
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.
I think all vectors are pointing in a direction that suggests that there are real explanations that it's not just
We changed vectors again, restraints gouging into my chest so hard it knocked the breath out of me.
and that are highly vectorized by micronutrients.
namely that's all the Google Translate, all the natural language processing, is based on a algorithm called Word2Vec, to map words into a vectorial form. And once you map words into a vectorial form, you can understand the machine.
But in chemistry, whenever you see NaCl, you see KCl a lot. So in vectorial space, they must be close to each other.
They're vectors . They're not independent.
They're vectors that look like this.
2,000 vectors . Because I don't want to be dealing with big matrices.
That works on the vectors as it did before.
But Thomson realized that the magnetic vector field B could be defined as the curl of some other vector field, the magnetic vector potential A.
Now even though they're both vector fields, it turns out that A is often much easier to work with than the magnetic field itself,
Now take a closer look at the vector potential.
But where do you find something like that? - Let's think about a really simple vector , say 1 in the x-direction and 2 in the y-direction. If I reflect this vector along the line y equals x and then reflect it about the x-axis, I get this.
To satisfy it, Einstein knew he had to use special mathematical objects called tensors. A simple kind of tensor is a vector . You can write a vector as a set of components multiplied by their basis vectors .
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. So the components, the numbers in this list, changed, but the vector didn't.
It stayed the same. 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.