Image and Kernel
ฝัง
- เผยแพร่เมื่อ 28 พ.ค. 2019
- 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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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!!!!!!
Definitely recommending this video to all my friends and future students studying Linear Algebra
Finally someone show what it actually means so you can understand what you are actually searching for, thank you!
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
Wow this is the best explanation of kernel and image on youtube, thank you so much Professor Dave!
Fantastic video! Far better explained than in my university lectures
People like you deserve great honor!!!
Totally awesome, I finally get it, thank you very much.
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.
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.
Professor Dave = Guaranteed success in academics!
This helped immensely and simplified the concept so nicely. Appreciate it
your explanation has been very concise.... awesome
Thank you, professor, you are truly a Mater. You can explain tough topics in a very easy way! Happy Holidays
Really well explained Sir. I'm grateful
My professor went through the definitions of kernel and image way too quickly in his not-recorded lectures. This saved me, thank you
Prof Dave, You are sweat heart of every students who loves mathematics.
Amazing, right to the point. Thanks!
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
Elegantly explained. Thanks a lot
For Dave and all the people that make these videos happen, thank you so much!
thankyou for this amazing
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 😁 👍✌
best video on image and kernel
Thanks Professor Dave.
Thanx Prof Dave!
Very nice teacher
this was very helpful
simple and amazing
Thank you
This guy just turned my last week's 1hr long linear algebra lecture into a 5 min video... Thank you!
Same lol
Thanks!
nice video, thanks alot
Thanks alot
i finally understand the kernel after soooo long
nice man great
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
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
If you give graphical representation of the transaction L : R^3 --> R^2, and pointing out the kernel, it would be useful.
Too sweet example love much
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?
Thank you, Great explanation! Coincidentally I have an exam about this next week
lmao, i have a final ToMORROW
Mine is on Friday
if the vectors of the form like wise is not given in the question how to find the image
Great...
Love your videos. Nice haircut btw. Looks great. Can you please make a few videos on calculus too
I made a 35 part calculus series, check it out!
@@ProfessorDaveExplains sure thank you
What is the difference of the Null space and the kernel then?
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.
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?
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).
Sir pls can you teach s..what is rank of matrix and how to find it
easily undersood whole lecture within 5 minutues
should'nt kernel be 0,0,0 for the last question as the transformation is from 2 to 3
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.
@@2kcurse438okie, 😃👍
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
Why is the rest of this course made private?
I release one per week!
@@ProfessorDaveExplains Good to know! Looking forward to the rest.
You are the English version of Elia Bombardelli for italian students
What’s happening?
GOAT
professor dave has saved another poor student's braincells! (me)
Second!
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...
sooooo, where does popcorn come from......i tihnk i missed a step
First view
First comment
First like
😘😘😘
thx, my prof is useless
No
not well explained, still confused
watch again