## VECTOR SPACES – LINEAR ALGEBRA

We introduce vector spaces in linear algebra.

#LinearAlgebra #Vectors #AbstractAlgebra

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*–Playlists–*

Linear Algebra: https://www.youtube.com/playlist?list=PLDDGPdw7e6AjJacaEe9awozSaOou-NIx_

*–Recommended Textbooks–*

Linear Algebra and Its Applications (Lay): https://amzn.to/37gBZ27

Linear Algebra Done Right (Axler): https://amzn.to/2T0GpBI

Introduction to Linear Algebra (Strang): https://amzn.to/3dC6kJq

Linear Algebra: Step by Step (Singh): https://amzn.to/2T33G65

3,000 Solved Problems in Linear Algebra (Lipschutz): https://amzn.to/3j2nJMw

In this video we talk about Vector Spaces and ask ourselves if some sets are vector spaces. We also talk about the polynomial vector space.

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Nice explanation

good video thanks

a polynomial with an non-integer exponent is not a polynomial btw

Thanks for this, I just started Vector Spaces and since I haven’t seen any examples of questions I wasn’t sure how it’s tested. I’m assuming the whole section is tested by proofs.

good

good

good

I don’t understand nothing ☹️

isnt deegre zero for polynomials the coefficient a_0 without the t variable? cause degree 1 is a_1*t. I think Axler defines the degree of the vector 0 in this case a negative infinity but I'm not sure. I actually came to this video after reading the sheldon axler book and being confused about polynomial vector spaces.

You saved my life

Thank you for saving my final exam with this now I can get an A

helll yeah dub.. thx Big Chrev

You sound like John krasinski!

Thanks you sir you are the best

One of the best explanation ever

should we draw?

This is a great explanation. Thanks.

This is a great explanation. Thanks.

thank you for good lecture

I am still confused, im still stuck in the physics definition of a vector.

Please share the link of your previous videos where you proved all these.

For the problem at 6:00, saying that if u=(-1,2) and (-1)(2) is not >= 0, this would be false right? As we cannot use a vector that is itself not in the W set?

Thanks

This is instruction is so much easier to understand comparing to my prof ! ! !

Great explanation Sir big thanks

What if you scale your p(t) by zero. doesn't that make the degree zero?(for the last statement you proved!)

Thank you for lectures btw.

I think you have to mention the >Field< over which you are defining these vector spaces.

Please I want a tutorial session

@8:58 Degree of a polynomial is always a positive integer, it cannot be in fraction. So that example is not a polynomial.

"If you've never looked at a polynomial before."…. c'mon dude. Know your audience.

Is it necessary that addition is defined for all elements of vector space..or it is enough that the sum of defined elements exist within vector space. Consider Set of all matrixes(including different orders)

I still don't get it … this is difficult for me

Better than my linear algebra prof. VeRy VErY HelPFuL! No reason to go to lectures.

So far the best explanation on proving vector spaces.

Thank you from nepal

could be better if you have a pointer on which part of the slide you're talking

Very helpful

Great video. Thanks.

Thanks

If two or three axioms are good enough to proof things, why we need to have ten?

(Y)

At 6:27,what were you saying 1 to the right 2 up and 3 to the left and 1 down? what does this mean?

very satisfied lessons