Image and Kernel

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Now that we've learned about linear transformations, we can combine this with what we know about vector spaces to learn about the concepts of image and kernel. Let's get a closer look!
Script by Howard Whittle
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Опубликовано:

28 май 2019

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Комментарии : 76

@arfinsyed 3 года назад

The most simple explanation that I have found on the entire Internet that explains Image and Kernel after searching for 2 weeks!! THANK A MILLION!!!!!!

@a.human. 2 года назад

Definitely recommending this video to all my friends and future students studying Linear Algebra

@danielmoss7133 3 года назад

Fantastic video! Far better explained than in my university lectures

@ahmadyogi1340 3 года назад

Wow this is the best explanation of kernel and image on youtube, thank you so much Professor Dave!

@ion9328 3 года назад

Finally someone show what it actually means so you can understand what you are actually searching for, thank you!

@JoseAlvarez-dl3hm 4 года назад

Totally awesome, I finally get it, thank you very much.

@Demon0228 6 месяцев назад

This helped immensely and simplified the concept so nicely. Appreciate it

@ranitchatterjee5552 3 года назад

People like you deserve great honor!!!

@geoffrygifari4179 5 лет назад

your explanation has been very concise.... awesome

@hcos8139 Год назад

Thank you so so much. Every time I have an exam I read the 70 pages with of chapters and I barely understand anything. 5 minutes of your video explains it PERFECTLY clear. Thank you so much

@phantorang 5 лет назад

Your haircut looks great, if you were wondering. Other than that, I got no idea what this is about, I guess I will have to read up on it 😁 👍✌

@just4simplegg428 7 месяцев назад

Thank you, professor, you are truly a Mater. You can explain tough topics in a very easy way! Happy Holidays

@lightok111 3 года назад

Really well explained Sir. I'm grateful

@sohamsantra7548 2 года назад

Professor Dave = Guaranteed success in academics!

@mladizivko Год назад

Amazing, right to the point. Thanks!

@animeshsinghal3405 2 года назад

Elegantly explained. Thanks a lot

@BO55 Год назад

Wow, what an explanation. Even after listening to my prof's video multiple times, didn't get this understanding. This video explained my doubts about why are trying to equate the L(s) = 0 to find the kernel in a pretty elegant way.

@__-ni1kz 2 месяца назад

Getting halfway through linear algebra and having the prof say "for those of you in engineering, this everything past this point isn't useful to you" really took the wind out of my sails. I hate having to learn these complex abstractions for no reason, when I could be spending my time studying for finals that have utilization in my field. Thank you for a straight forward explanation, once we exited euclidean vector spaces the math became harder to conceptualize.

@kmishy 3 года назад

Prof Dave, You are sweat heart of every students who loves mathematics.

@syunegevorgyan Год назад

O thank you. You can't even imagine how you helped me. I was about giving up when I saw your video and I started to understand this theme. thanks very much again

@DheaFikyFatchaturRizky 4 года назад

thankyou for this amazing

@lukevillanueva1494 Год назад

My professor went through the definitions of kernel and image way too quickly in his not-recorded lectures. This saved me, thank you

@Firelord375 Год назад

For Dave and all the people that make these videos happen, thank you so much!

@abhijitdeokule1986 2 года назад

best video on image and kernel

@CSBPRAKASHDEEPAK 7 месяцев назад

Thanks Professor Dave.

@curtpiazza1688 2 года назад

Thanx Prof Dave!

@nghiatrinh8753 3 года назад

this was very helpful

@hamzamehmood4099 5 лет назад

Very nice teacher

@mehdimansouri1547 11 месяцев назад

simple and amazing

@khamishoufar1019 3 года назад

in machine learning, we have a concept of the kernel in the context of similarity measure between two observations! what is the intuitive explanation about that ..Thanks

@kimkakyeong 2 года назад

This guy just turned my last week's 1hr long linear algebra lecture into a 5 min video... Thank you!

@Harminder_Saini 2 года назад

Same lol

@anky137339 3 года назад

Hi All , What is the intuition for having Kernel mapped to space W is 0 ? is this shows 0 loss of information when transformed ? AND this is great video explaining concepts in 5 mins

@nomaetamamo6479 11 месяцев назад

nice video, thanks alot

@jademath910 2 года назад

If we have two linear operators on n-dimensional vectors space, say f and g what would be the image(f+g), image f , and image g? can we say that image f = image g?

@catalinaionascu171 2 года назад

Thank you

@put.7070 2 года назад

Thanks!

@KidNamedVashin 5 лет назад

Thank you, Great explanation! Coincidentally I have an exam about this next week

@ysabellarivera8166 3 года назад

lmao, i have a final ToMORROW

@aurumstinger4479 2 года назад

Mine is on Friday

@aishwaryabimaljoy6642 3 года назад

if the vectors of the form like wise is not given in the question how to find the image

@vaishnavisharma9467 5 лет назад

Love your videos. Nice haircut btw. Looks great. Can you please make a few videos on calculus too

@ProfessorDaveExplains 5 лет назад

I made a 35 part calculus series, check it out!

@vaishnavisharma9467 5 лет назад

@@ProfessorDaveExplains sure thank you

@Ahmedibrahim0100 2 года назад

Thanks alot

@ranbirsingh494 5 лет назад

nice man great

@tadabae 3 года назад

i finally understand the kernel after soooo long

@ts.nathan7786 9 месяцев назад

If you give graphical representation of the transaction L : R^3 --> R^2, and pointing out the kernel, it would be useful.

@sgtivo7330 4 года назад

This gets super funny if you watch it at 1.5x the speed... given you already understand the Concept and your head doesn't start smoking.

@TheSmartgutt Год назад

What is the difference of the Null space and the kernel then?

@sajithpriyankaragunawardan4530 3 года назад

Too sweet example love much

@mohammadidreesbhat1109 Год назад

Great...

@DogeCharger 4 года назад

Quick question: If I understand kernels correctly, then that means that the Dimension of them will generally be 1? And the Dimension of an Image will generally be what it is equal to -- so if it equals ax^2+bx for example, then the dimension will be 2?

@johnmccrae2932 4 года назад

It turns out that the dimensions of the image of a linear map and the kernel of a linear map depend on a property of maps called "rank". Pretty much, if you think of a map as a matrix multiplying a vector in the domain, the rank is how many of the matrix's columns are linearly independent (not multiples of each other). The dimension of the image is the rank, and the dimension of the kernel is the number of columns in the matrix minus the rank. Definitely check out Gilbert Strang's linear algebra lectures on MIT OCW if you want to know more (I realise my explanation might be quite dense).

@nabanitagoswami6652 5 лет назад

Sir pls can you teach s..what is rank of matrix and how to find it

@bartman999 5 лет назад

Why is the rest of this course made private?

@ProfessorDaveExplains 5 лет назад

I release one per week!

@bartman999 5 лет назад

@@ProfessorDaveExplains Good to know! Looking forward to the rest.

@gunjansharma6603 6 месяцев назад

don't tell me i skipped one test and tried and gave up on this topic three times only to learn it in 5 minutes whaaat

@wecanplay5363 Год назад

should'nt kernel be 0,0,0 for the last question as the transformation is from 2 to 3

@2kcurse438 3 месяца назад

By definition , set of vectors in R2 that give 0 vector in R3 will be the kernel. That is why because these vectors are from R2.

@wecanplay5363 3 месяца назад

@@2kcurse438okie, 😃👍

@bella-rp2rw 2 года назад

You are the English version of Elia Bombardelli for italian students

@bimsara3824 2 года назад

easily undersood whole lecture within 5 minutues

@leekimjinyoon4473 5 лет назад

What’s happening?

@the_gis_madiam Месяц назад

professor dave has saved another poor student's braincells! (me)

@salamlababidi3042 Год назад

GOAT

@jamesevans2211 5 лет назад

Second!

@ronycb7168 Год назад

always at .8 or .75 X prof just commented here attendance and for the posterity of mathkind. bad word play sorry but in a hurry to finish this stuff already too late...