Image and Kernel

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

Check out "Is This Wi-Fi Organic?", my book on disarming pseudoscience!

[arfinsyed]

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

[phantorang]

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 😁 👍✌

[ahmadyogi]

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

[lukevillanueva]

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

[sohamsantra]

Professor Dave = Guaranteed success in academics!

[BO]

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.

[ranitchatterjee]

People like you deserve great honor!!!

[Demon]

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

[syunegevorgyan]

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

[geoffrygifari]

your explanation has been very concise.... awesome

[DogeCharger]

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?

[nabanitagoswami]

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

[gunjansharma]

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

[ronycb]

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...

[a.human.]

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

[JoseAlvarez-dlhm]

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

[sgtivo]

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.

[kmishy]

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

[danielmoss]

Fantastic video! Far better explained than in my university lectures

[vaishnavisharma]

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