What is...an affine space?

Goal.
Explaining basic concepts of linear algebra in an intuitive way.

This time.
What is...an affine space? Or: I lost my origin.

Warning.
There is a typo on the fourth slide, as pointed out in the comments. The "green matrix" should be {{-1, 0}, {0, -1}}. Also, a + 0 = a (typo at 9:45), see comments. Sorry for that.

Slides.

#linearalgebra
#algebra
#mathematics

[thinkmachine_]

I was looking for an intuitive explanation on affine spaces and found this video, I thank you for all that you put into making these videos.

[curiouscraw]

Great video, helped me to finally get a sound understanding of what my professor means when he describes affine geometry as geometry where they lost the origin. Thanks!

[Agus-ofrh]

Thank you, I needed some visual explanation to feel the subject "more alive" (showing "movement"), and your video did that for me.

[Karim-nqbe]

a + 0 = a (small typo at 9:45). Thank you, always a pleasure to come back to your channel :-)

[vivaangupta]

The first matrix (on the left) at 10:49, I believe, doesn't correspond to the picture associated with it. The "linear part" of the matrix given is a -π/2 rotation (counter-clockwise) and it appears to me that the picture associated with it in this video is a π rotation (counter-clockwise).

[almspb]

Well, proper and highly quality explanation. Thank you very much.

[anandpaladhi]

thank you...this helped me to understand the concept in much better way...though, could not follow "Matrices for affine maps" at 10.48 but probably need to learn little more and come back here again to revise...

[lowerbound]

Great Explanation as always 😻 Thank you!🙏🙏

[Victual]

I watched it till the end; it's too good not to subscribe!

[jonathanlister]

Well, Thanks for your response. I have to say that I did find your presentation to be excellent, especially your graphical work. I suppose time is a factor in these presentations and you have to be selective in what you present as an introduction to Affine spaces! I did not mean my comment as a criticism. Yours Jonathan.

[jeanphilippepuyravaud]

Very useful. I saw the comment by AK. For me, your accent is fine, but you tend to lower your tone and volume at the end of the phrases. So it looks as if the important point is xxx.

[MathCuriousity]

Hey question if you have a chance: why are we taught vector spaces and then affine spaces? Is there a way to define an affine space without talking about a vector space? I feel like I need a different way of thinking about affine spaces and I don’t like the idea of using vector spaces minus some vector property to get affine. Help me please understand a definition of affine space without vector space!

[MathCuriousity]

One other question: could you explain what some professors mean when they talk of Euclidian affine space and euclidian vector space as opposed to just affine spade and vector space? Thanks so much!

[mangaart]

Thank you for this video it helped me a lot!

[khoanguyen]

Is affine space a larger set than vector space? or it is like a 'dual' of a vector space?

[xoppa]

how do we go from an 'affine space' in geometry where there is no origin, to an 'affine transformation'.
awesome video

[jonathanlister]

Very interesting, however I rather think you have over-stated this no origin stuff, the point is there is no preferred origin. Also why not mention that contrary to the Euclidean geometry battered into our skulls at school, the distance between two points or the angle between two lines need not be significant. We should refrain from introducing either magnitude or direction as they are invariant concepts for us in this space.

[Labroidas]

This is a great video, but if I may give a small critique: it's sometimes hard to understand what you're saying, mostly i think because the microphone you're using is pretty low-quality, the room you're in has a strong echo (the sound is reverberating off the walls), and you're speaking fast and are sometimes not enunciating enough.
Nevertheless you're amazing at explaining, it helped me a lot, thank you so much!!

[seka]

Wow. I have changed unlike to like. the example at 8 min gives more than hundreds of videos on youtube

[AK-cyql]

even with subtitles, your accent was difficult to understand