Mod-02 Lec-08 Vector spaces

[saitejaveeragani]

don't know why there are many negative comments. at least appreciate their efforts for trying to teach students at free of cost. and those who are frustrated, ask your university professors to teach properly as you are paying them.

[pyrole]

Thanks again for a great lecture. To all the negative comments, there are some prerequisites to studying this e.g. Fields, basic calculus, knowledge of functions etc. If you don't understand these basics, you will struggle to understand the topics. Otherwise this is a great material.

[creativelearningacademy]

Top class Faculty. Huge respect sir. I love the way you think, imagine and talk. Many faculties have memorized the content since they are teaching it for years.

[kg]

Very very thankful to you sir, it's not about the basics of vector space, but the explanations of yours for each example was really good, and really affected my interest👍

[nothingisimpossible.]

We all are lucky which gives me one of the best opportunity to learn higher mathematics free of cost so thank u all team of nptel

[chaitalipatil]

yes its true Sai Teja Verragani...
all the bad commentators who watched the video are the ones who don't give attention in their college lectures inspite of paying them.

[kingvenkat]

He is teaching in such a way that students and professors the both have same knowledge 😀😃

[ShashankChoudharyIITD]

For a set of polynomials of exact degree 2 to be a vector space, it would need to be closed under addition and scalar multiplication. However, as shown above, adding two polynomials of exact degree 2 can result in a polynomial of a lower degree, and multiplying a polynomial of exact degree 2 by zero results in a polynomial that is not of exact degree 2. Hence, the set of polynomials of exact degree 2 does not satisfy the axioms of a vector space.

[srayachakraborty]

Sir thanks, it's really helpful, but i have a objection that the THE CAMERA IS MOVING CONTINUOUSLY it is creating problem to focus on the notes.👍

[kushagr]

One of the best teachers I have ever seen!

[SKPGenius]

Thanks a lot of sir , u are just like a GOD for us...🎉

[joininorcut]

answer for the 16th example:
Is it because addition of any two polynomial of degree 2 will not yield zero?

[tsvmanojturlapati]

Thank You Sir.I wish God bless you with good health and wealth .nice teaching.all doubt's are vanished.

[powerentertainment]

Why people be negative on this guy, all my professors in my college in India they don't even teach anything and they know nothing about their subject
At least this guy is trying, ...

[priyanshubansal]

the reason that vector space always contain zero is that zero is additive inverse element under addition operator over field /R which is necessary because every vector space is an example of group theory and every group has property of having identity element in it . so that's why 15th example was not vector space ...as i mentioned that every vector space contain additive inverse element under addition operator .

[dharapatel]

Nice lecture sir.
I have one question.
V= R^2
(x1, y1) +(x2, y2) = (x1+x2 y1+y2)
K(x, y) =(2ky, 2ky).
Then set V satisfied 1(x, y) = (x, y)?
Please reply me.

[rddegreeyt]

Every vector space must contain 0 in it
Vectors can be multiplied and add mean we can take their linear combinations
and the vector addition and multiplication behave in a reasonable way then whatever the collection is, is a vector space

[yashdand]

X, y belongs to v should be written about commutative and associative property

[micman]

what is the meaning of vector space V over field F??

[priyanshubansal]

in telling axioms of vector space he cared about group theory that nice