Lecture 9(A): Euclidean Space

Norm, distance, Triangle Inequality, dot product.

[vadiquemyself]

distance looks absolutely the same as length, both being the “norm” of a vector, and since the vector subtraction is defined (where and how by the way?) is there any reason to distinguish distances and lengths?

[MathCuriousity]

Professor please help me: I was told a Euclidean space is just a affine space with an inner product space. Does an inner product space automatically mean the Euclidean space is also a norm/metric space? If it doesn’t automatically assume this, what exactly can we do on the space if it’s just an inner product space (without being normed/metricized)?

Finally - if we do assume inner product means normed and metricized space, does this then mean we can add/multiply vectors, measure lengths, measure distance between points, add a point to a vector (although not add point and another point - which I geuss doesn’t even make sense in a vector space anyway let alone affine space). Thanks!!!!

[longweicheng]

Absolutely brilliant! Thank you sir for your whole lecture series. Great for Econ/Finance PhD students with weak math foundations. Can we get the exercise on your personal website? It would be very useful!

[riyadbarka]

thank you, this actually looks so easy wow, wish you we're my teacher

[ulvidilov]

Thank you very much !! Hello from Azerbaijan

[Hi_Brien]

Hahaah, I like how I get an answer to a question from my home state XD