I think you confused linear independence with orthonormality in the verbal definition. We say that two vectors are orthogonal if their inner product is zero. Linear independence doesn't suffice for this as for example (1, 0)^T and (1, 1)^T are linearly independent, but (1,0) • (1,1)^T = 1 and not 0. I love your content btw, just wanted to point that out.
Was going to comment the same point. Linear Independence just means that one vector is not a linear combination of some other vector(s). Doesn't mean the dot product is 0.
May I request a video explaining how L1 regularization creates a sparse matrix? I have already read a few articles on the internet, but I still couldn't convince myself to fully understand the process. Your explanations on data science topics are consistently clear and concise, and I am eager to watch a video on this specific topic soon. Thank you for providing such valuable content on TH-cam.
2:46 why linear independence means that dot product is zero? for example, vectors (1, 0) and (1, 1) linearly independent, but their dot product is 1*1+0*1 = 1 != 0. As I understand dot product is zero for orthogonal vectors
This took me ages (and a lot of pain) to understand in my Multivariate Statistics class. I wish this video would have been around then... Possibly I find this video so good because I have already learned the basics, but I think this was probably the most understandable explanation of Orthogonal Matrices and PCA I have ever heard. So... tanks! 😅
thank you for teaching/refreshing us the algebra in relatively short sessions. if possible, please include a numerical example in these videos. i love the topics you choose.
Such a high-quality video! I was very uncomfortable when studying these theories without knowing the principles and finally I found this video to help me clearly figure out how these theories were worked out! Thank you so much!
I think you confused linear independence with orthonormality in the verbal definition.
We say that two vectors are orthogonal if their inner product is zero. Linear independence doesn't suffice for this as for example (1, 0)^T and (1, 1)^T are linearly independent, but
(1,0) • (1,1)^T = 1
and not 0.
I love your content btw, just wanted to point that out.
Was going to comment the same point. Linear Independence just means that one vector is not a linear combination of some other vector(s). Doesn't mean the dot product is 0.
thanks for the correction! I'll put this note in the video description
Unintended pun....sits squarely.....
haha!
May I request a video explaining how L1 regularization creates a sparse matrix? I have already read a few articles on the internet, but I still couldn't convince myself to fully understand the process. Your explanations on data science topics are consistently clear and concise, and I am eager to watch a video on this specific topic soon. Thank you for providing such valuable content on TH-cam.
2:46 why linear independence means that dot product is zero? for example, vectors (1, 0) and (1, 1) linearly independent, but their dot product is 1*1+0*1 = 1 != 0. As I understand dot product is zero for orthogonal vectors
This took me ages (and a lot of pain) to understand in my Multivariate Statistics class. I wish this video would have been around then... Possibly I find this video so good because I have already learned the basics, but I think this was probably the most understandable explanation of Orthogonal Matrices and PCA I have ever heard.
So... tanks! 😅
This channel is awesome. Subscribed
thank you for teaching/refreshing us the algebra in relatively short sessions. if possible, please include a numerical example in these videos. i love the topics you choose.
Noted!
Such a high-quality video! I was very uncomfortable when studying these theories without knowing the principles and finally I found this video to help me clearly figure out how these theories were worked out! Thank you so much!
Hi, Great video, Could you talk about the Gaussian Process in future videos? thanks very much.
@ritvikmath Hi, can you put more insight on condition no. of orthogonal matrices n how it can deal with noise?
Nicely explained!
Great video :)