Lecture - 1.1 Vector Spaces

[@epistemophilicmetalhead9454]

set of all scalars is a field of scalars (usually set of real numbers) vector space: set V where if two vectors belong to V, addition and scalar multiplication of those vectors will also belong to V. elements belonging to vector spaces must satisfy commutativity, associativity, additive and multiplicative inverse and identity, distributivity

[@EdWitten-rq9bz]

Multiplicative inverse isn't an axiom of a vector space.

[@jagadeeshkumar2091]

10:45 - Definition of Vector Space - Part 1 15:45 - Definition of Vector Space - Part 2 31:20 - Summary

[@vijayaramamurthy5802]

Excellent Lecture Sir. Thank you for all the great work!!!!

[@abhishekrajvir66]

finnalyyyy i properly understood vector spaces , beautifully explained

[@patheyshah6731]

Very nice lecture 👍🎉

[@Amit1994-g9i]

Sir, is a vector space with with one component only, is same as a scalar?

[@AdithyaIIT-J]

obviously not you will still have a direction component its just as If 0 and 0 vector are the same thing but they aren't r8

[@rickmoulikxia0448]

Sir aeta ki Calcutta University er jonno follow korte pare for nep sysyter senester 2 minor plz bolun sir

[@SamratKar]

Sir, if a arbitrary set V is known as Vector space for which the two operations - scalar multiplication and vector addition is defined with the properties you have explained, then how we define the cross product operation in the same space? Is this third property (vector multiplication) not a necessary condition for the definition of V?

[@EdWitten-rq9bz]

Think about cross product in 4 dimensions. It doesn't exist. So R4 will not be a vector space if we include vector multiplication.

[@mohantyabhijit9755]

sir can we get the notes (notes u are writing)

[@ahairshi]

drive.google.com/drive/folders/1yHaHWNk1NIIrxGFnDgqGGCdL3dc3Q7Rb

[@Amit1994-g9i]

Another property should have been there I guess, 0.v=O where O is the zero vector

[@HJohannes93]

Not really, he is giving the definition of a vector space. The property you mention is not part of the definition, but is a consequence of the definition. Indeed, 0v = (0+0)v = 0v + 0v, and adding the additive inverse of 0v to both sides gives you the result.

[@ThakursBoy]

1 done✓

[@shivanipal8482]

Sir can you give me my 3 question solution s please

[@tpsicmin]

Clear Sir

[@abhijeetsalve3064]

You really need to improve your teaching so that a average person could understand what are you teaching...whats closed uner multiplication? What is a vector? What iis the simple definition of vector space which you failed to explain i can assure you that ...really

[@StupidMeYesterday]

what is definition of vector space according to you? what he said is the mathematical definition, sets whose elements(vectors) can be added and multiplied. if your imaginining a definition with direction and magnitude you're in the wrong class, this is math.