A Swift intro to Geometric Algebra (2020) [video]
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Re: A Swift intro to Geometric Algebra (2020) [video]
#2The geometric algebra over linear algebra people vs the tau over pi crowd. The two at 80km/h, who is faster?
Re: A Swift intro to Geometric Algebra (2020) [video]
#3The geometric algebra over linear algebra people vs the tau over pi crowd. The two at 80km/h, who is faster?
Not really?
Re: A Swift intro to Geometric Algebra (2020) [video]
#4Great video!
Re: A Swift intro to Geometric Algebra (2020) [video]
#5I am a bit confused hearing a vector is one dimensional. The way we represent a vector (x,y) or (r,θ) sounds like two dimensions to me.
Re: A Swift intro to Geometric Algebra (2020) [video]
#6The geometric algebra over linear algebra people vs the tau over pi crowd. The two at 80km/h, who is faster?
Not really?
It's "four Maxwell equations" vs. "one Maxwell equation". Technically they allow to do the same, the argument about convenience and maybe underlying connections which aren't that visible in linear algebra but more pronounced in geometric algebra case.
Re: A Swift intro to Geometric Algebra (2020) [video]
#7I am a bit confused hearing a vector is one dimensional. The way we represent a vector (x,y) or (r,θ) sounds like two dimensions to me.
It's a more abstract kind of dimension. The vector is only one dimensional because it has a factor of one unit vector (only one associated "direction". A Bivector has two factors of unit vectors to describe a 2 dimensional region.
That's independent of the dimension of the space it's embedded in. So you can have a one dimensional vector in 2space, 3space, nspace etc. But it only ever describes one direction, an oriented line.
Re: A Swift intro to Geometric Algebra (2020) [video]
#8The capitalization on here made it look like it was in Swift.
Re: A Swift intro to Geometric Algebra (2020) [video]
#9I am a bit confused hearing a vector is one dimensional. The way we represent a vector (x,y) or (r,θ) sounds like two dimensions to me.
geometrically, a vector is direction that points from one point to another -- it is one-dimensional, like a line between the two points.
Re: A Swift intro to Geometric Algebra (2020) [video]
#10I am a bit confused hearing a vector is one dimensional. The way we represent a vector (x,y) or (r,θ) sounds like two dimensions to me.
In a 3D space, a vector would be (x,y,z), in 4D (x,y,z,w), etc.
"One dimensional" simply means a vector is a straight line, as opposed to a plane or a solid.