Thank you so much! I'm thrilled it helped clear things up! I had my own 'what on earth is happening?' moment with Gram-Schmidt, so I figured, why not make a video to save everyone else from the confusion? Turns out, space vectors are a lot more fun when they’re not just floating in abstract math land! 😄🚀
I understand how they are created now. But How are the orthogonal vectors related to the original u, v, and w ? Any special meaning behind it ? Thanks.
Ah, great question! The vectors u′,v′ and w′ are like the cool cousins of your original u, v, and w. They span the same subspace as the originals but with a twist: they’re mutually orthogonal (a fancy way of saying they’re at perfect right angles to each other in vector and inner product terms). It’s all about keeping things neat. Hope that clears it up!
@@bigsigma1 I understand orthogonality comes up a lot in linear algebra and solving system of linear equations. Can you help me to understand how orthogonality makes it easier to solving large system of linear equations? Thank you very much.
Yes, it is the process in the space after all. Each iteration brings the vectors closer to their desired orthogonal form, refining the basis step by step
Visualisation always helps understanding these abstract concepts, thank you!
Happy to help! Abstract concepts without visuals are like soup recipes without measurements-confusing and likely to end in chaos!
Wonderful animation and very helpful to visualize Gram-Schmidt for 3 vectors.
Thank you so much! I'm glad the animation helped bring Gram-Schmidt to life!
@@bigsigma1 A comment I left 9 years ago on a 52 second video. What happened buddy, why you replying now?
Ah, TH-cam just brought this back for me now. Guess it want us to relive some nostalgia. Better late than never, right? 🙃
@@bigsigma1 Haha no worries. Thanks for helping me better understand Gram-Schmidt 9 years ago.
The video ends as soon as I'm starting to jam to the song.
I feel you! It's like just when you're starting to jam to the song, the vectors dance off into the sunset and the video ends!
better than hour long lectures on the topic, ty
Thank you! I'm glad this helped more than the long lectures-I believe that short and sweet is the way to go!
This is so much help for understanding how the process works, thanks!
Ah, the process reveals itself to those who seek ... 🙃 There’s much more beneath the surface.
Thank you for this video! its so much better now
Thank you so much! I'm thrilled it helped clear things up! I had my own 'what on earth is happening?' moment with Gram-Schmidt, so I figured, why not make a video to save everyone else from the confusion? Turns out, space vectors are a lot more fun when they’re not just floating in abstract math land! 😄🚀
Thx this open my mind a little bit further
You're so welcome! I'm really glad to hear that-it’s great to know it helped expand your thinking a bit more
I understand how they are created now. But How are the orthogonal vectors related to the original u, v, and w ? Any special meaning behind it ? Thanks.
Ah, great question! The vectors u′,v′ and w′ are like the cool cousins of your original
u, v, and w. They span the same subspace as the originals but with a twist: they’re mutually orthogonal (a fancy way of saying they’re at perfect right angles to each other in vector and inner product terms). It’s all about keeping things neat. Hope that clears it up!
@@bigsigma1 I understand orthogonality comes up a lot in linear algebra and solving system of linear equations. Can you help me to understand how orthogonality makes it easier to solving large system of linear equations? Thank you very much.
absolute cinema
Absolutely, it's like where the vectors are the players and the Gram-Schmidt process is the director, guiding the scene to perfect orthogonality!🙂
It helps me so much to understand the process from geometric point of view. Thanks a lot!
I'm so glad it helped! Understanding it from a geometric point of view is crucial-don’t miss out on these insights! Keep going!
Really helpful animation thank you for creating it ,easy to understand
You're very welcome! I'm glad the animation helped. I believe that Visuals can simplify complex concepts, making them much easier to grasp.
This is just 3 iterations of the process correct?
Yes, it is the process in the space after all. Each iteration brings the vectors closer to their desired orthogonal form, refining the basis step by step
Great visual explanation!
Thank you so much! I'm thrilled the visuals helped bring everything to life-it's always amazing when a concept clicks!
Great animation. Thanks.
Thanks so much! I'm glad you enjoyed it
A really good aproach thanks! :-)
Ah, the right approach is like a door-once you open it, the journey begins. Glad it resonated with you.
clear animation! Thanks!
Glad you liked it! I am always happy when this animation brings everything into focus so clearly!
tyty
You're very welcome! 😊
Traum
Yes, this animation was inspired by my dreams about vectors. 😉
I’m so glad you liked it-thank you for the kind words!
i can not hear u
I do not talk in the movie, I just let the vectors dance following the music-hope you can hear their groove! 🙂