02 - Must-learn optimization concepts - Hyperplanes and halfspaces

In this video we will learn three different ways of understanding of a hyperplanes. The first way of understanding is analytical and the two other ones are geometrical. We will see a hyperplane is the solution set of a
linear equation. Geometrically, it can be interpreted as an offset, plus all vectors orthogonal
to the normal vector. We also learn that hyperplanes are affine sets. Once you learn the concept of a hyperplane you can easily understand a halfspace. Halfspaces are not affine sets but they are convex sets.

Link to exercise 2.5 about hyperplanes:

Links to exercise 2.5, 2.6, and 2.7 about halfspaces:

[mohamedayman]

Thank you for your useful and interesting content. Please go on and continue the optimization concepts. thanks

[cipherswami]

aT*x = projected length * length of 'a' vector. Here length of 'a' vector is constant, so things worked fine, even aT*x is consider as just projection length.

[KKumar-xnzf]

Hey great lecture sir, please put make some more videos on the optimization topic sir . thank you

[nurankhattab]

how's vertical [1 2]T is aT, isn't it a directly?

[davemayy]

Mohamed is right. Dont stop yoh were strezzed out here