Mod-02 Lec-08 Vector spaces

[@saitejaveeragani4787]

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.

[@gsureshkumar7563]

Hmmm....

[@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.

[@3rddegreeyt144]

i still didnt get this fields concept can you plzz refer some good videos on this topic plzz

[@Dhruba-t7n]

​@@3rddegreeyt144A field F is just a set of numbers where addition and multiplication is commutative and associative and for each non zero number x in F,there exists inverse elements (-x) and x^-1 such that: x+(-x)=0 and x.x^-1=1.Also there exists unique element 0 and 1 in F such that x+0=0;x.1=x.

[@kg3217]

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.1357]

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

[@creativelearningacademy6929]

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.

[@chaitalipatil7909]

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.

[@kingvenkat6064]

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

[@kg3217]

No, he has told the basics, and yes, at later part, it is a little high, lekin wo kaphi samajhne wala hai, and those who understood will appreciate it!

[@tapabratasarkar8392]

Finally found the right channel...🙏

[@amlankumarsahu8716]

Best explanation ever

[@kushagr0123]

One of the best teachers I have ever seen!

[@learntoearnstockmarketworl7323]

Bhai is this course for M. Tech?

[@priyanshubansal6776]

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 .

[@tsvmanojturlapati4492]

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

[@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.

[@powerentertainment719]

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,...

[@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?

[@shubhamtrivedi7860]

Bro i think here closure property doesn't hold as sir said exactly degree 2 not less than 2..am I right

[@shahreyarhossain4406]

Addition of any two polynomials of degree exactly 2 may not always give you a polynomial of degree exactly2. Eg: x^2 +1 & -x^2 +1 are two polynomials of degree 2...but when u add them........!!! . So the set isn't closed under addition.

[@amardeepsingh1204]

awesome lecture guru dev

[@3rddegreeyt144]

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

[@srayachakraborty6167]

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.👍

[@dharapatel122]

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.

[@r1e2y4]

Hey Dhara! The line you wrote "K(x,y)=(2ky,2ky)" is not correct it should be K(x,y)=(Kx, Ky) but you have to state that K is a scalar in R then that will satisfy "1(x,y)=(1x,1y)". The way I was taught is that you have to verify all operations of vector addition and scalar multiplication from the list that the professor showed earlier.

[@micman4856]

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

[@yashdand7885]

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

[@angshukNag]

At 9:30 .. is the multiplicative inverse missing

[@ketan9318]

No, multiplicative inverse has been taken care of since it is a scalar and hence comes from field. It is not required for V. It is required for F.

[@ketan9318]

To have clarity, there are 2 operations in field(addition and multiplication), and there are 2 operations in V. Vector addition and SCALAR multiplication. The last 2 operations are performed on (2 vectors of V) and (one from F & one vector from V) respectively. So multiplicative inverse does not exists in SCALAR multiplication operation in Vector space V.

[@priyanshubansal6776]

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

[@laxmanpadamati]

What are you studying now

[@mohdsuhail422]

@@laxmanpadamati can you help me in linear algebra?

[@3rddegreeyt144]

16:24 so this is what Descartes want

[@gyanganga247]

properties of direct products k bare me bataye SIR ji

[@UPSC2025-MATHS.OPTIONAL]

Tq sir🥰

[@prabhakarraj7247]

may u plz xplain the meaning of vector spac?

[@ankushreddy6896]

its a space where you can add two or more vectors or scale them,the resulting vector will be in that same space.

[@Ashley_black-h3r]

Tamilan da

[@suneeshlalsurendran5289]

Helpful

[@LakshmiPathi434]

sir, we can know by reading books what did you write on the board. I need not it. what I want is "what is vector space how we can imagine it in physical way". please don't spoil our education by this way

[@meghrajchiniya6539]

ya bro,he is simply writing on board

[@manuhegde4905]

@Lakshmipathi Avula : Quality of your english gives some idea about the extent to which you can understand maths literature! Go through the very first and second sentence( if I can say so) of your comment. You may conclude that your education is spoiled already. He is an able teacher and is guiding many students here at IIT-Madras. If you start solving the problems(at all!) of mathematical physics, you may realize the significance of these profound concepts. All most all of us can understand his presentations very well and we've used it in our research projects.

[@dipti3463]

Lakshmipathi Avula 😶😶

[@joyda_dark_horse6677]

he is simply writing away notes from some book without giving the physical picture of vector space

[@r1e2y4]

Try watching these videos. I think they give a great interpretation of vectors spaces, span, basis, etc! kzbin.info/www/bejne/nH_OkK2wlrKiidU

[@nagaraju332]

excellent sir,

[@ANGEL-mb9yx]

Good keep it up

[@dipeshkumargupta750]

Videomaker is unskilled, It was really not expected by NPTEL. Even more than 50% of video quality on NPTEL is very bad. Even the professors are careless about it. Why you just give such prestige of IIT's to such person. I am also in IIT, its shameful for me also.

[@remayne677]

@@prateekmishra6245 Its his choice.

[@virtualrendezvous2220]

Look at yourself before saying to someone else...u r in IIT bcz of reservation...u r also unskilled and undeserving..u stole someone else's seat

[@varun_4125]

@@virtualrendezvous2220 bruh you just assumed his caste based off of a comment

[@maheshwarimukesh8115]

Plz sir provide video in hindi

[@xoxo5091]

thanks

[@obviousness251]

He is just copying the book and spitting!! Such a shame!!

[@vivekkumar-vp5qr]

why dont u try to deliver a lecture standing over there if u r so proficient??oh,my mistake!! u will not even get a chance to reach there.

[@siddharthchoudhary1812]

I hardly understood anything in this lecture...I'm not discouraging the teacher it's ki I think the explanation is a bit difficult to understand.

[@samueldkhar613]

Try rewatching twice or thrice

[@samueldkhar613]

This is the best video lecture on linear algebra from my experience

[@kingvenkat6064]

Explanation is too worst

[@thehacker738]

Unfit to teach Mathematics. Resign; Go and teach Humanities. Its maths man. Not blah blah blah notes. nalla vela unna mari maths sir ennaku illa athanala than maths la 10th la 99% eduka mudinjithu

[@adityajoshi1606]

and yes this section of maths is 60% theory

[@xoxo5091]

thanks