Direct Sum

Have you ever wondered how to sum two mathematical objects in an elegant way? Then this video is for you! In this video, I define the sum of two vector spaces and show something neat: If you add two bases together, you get a basis for the direct sum! Finally, I generalize this notion to direct sums of n vector spaces. Enjoy!

[volcanic]

I wish I could have professor like Dr. Peyam

[youurdream]

Watching you doing the linear algebra stuff is like re-living my time at uni, where Albee’s was my favourite. Ah beautiful times, so much nostalgia. 😭😭

[jorgepedreirapedreira]

Dr Peiam it is the correct position to your whiteboard. Now we are seeing so good your amazing lessons and lectures

[willcollings]

Holy cow, this was fantastic. Wish every professor was as good as you!

[kaikleinbard]

love your upbeat teaching style, and clear examples

[danielaorozco]

I can only imagine how cool a conversation with you would be :0 today I finished the last math class of my career and I had to admit I started crying 😢 it feels like I lost something very important. you’re all I’ve got left until I graduate and make my masters (which will of course be math related) math has always been my happy place and I’m so grateful for people like you that take the time to teach ❤️❤️ amazing job thanks for everything!

[roeetoledano]

amazing, thank you so much! you explain the material so well

[mihaelaangelova]

it's BASED :D. I didn't expect that coming.

[ronpearson]

So how does the direct sum relate to exclusive gates XOR XNOR? They use the direct sum symbol as the algebraic equivalent to the truth table.

[lacanian]

this was a really good explanation, thank you!

[timurbabaev]

Please make a video about characteristic polynomial and trace of matrix!

[indumathikrishnappa]

I am very happy when I listen ur voice

[Gaelrenaultdu]

Hello, i had a question. What makes us suppose the only intersection is the zero vector ? The following proof is right, but only assuming W inter Z = {0}. How do we proof this is the case, how do we prove that the only element in W inter Z is the zero vector?

[sayanjitb]

Dear sir eager to know more about the general version of "Direct Sum"!

[rodrigocalixto]

How could we prove this without assuming that V is finite dimensional?

[newtonnewtonnewton]

Thanks a lot D peyam ramadan kareem رمضان كريم السلام عليكم

[navierstokes]

Why do you hate Axler's Linear Algebra Done Right?

[cmplstofB]

By the way, your wallpaper is cool. It is Ukiyoe, isn't it?

[debasisbehera]

Let A and B be subspaces of R^3 defined by
A={(x, yz)€R^3/x=y=z}, B={(0, y, z)/y, z€R}
Prove that R^3=AdirectsumB.


Solve this for me.