Linear Algebra 3 | Linear Combinations and Inner Products in ℝ²

[@sylvanfranklin6904]

This is a great explanation of Linear. I tried to learn via 3b1b's video series, but I like yours better because they feel more geared toward math majors, with proper notation and less abstract metaphors! Great stuff!

[@brightsideofmaths]

Thanks a lot :)

[@gradientcube]

You have a great voice and explanations

[@brightsideofmaths]

Thank you so much :)

[@3.12Q]

Thank you so much 🙏🏻 you explain so well that a highschool student can easily understand! Thanks again ❤️

[@brightsideofmaths]

You are so welcome! :)

[@johnitaballmer3966]

Thank you.

[@nucreation4484]

The way you presented the orthogonality around timestamp 6:07 is interesting. Is there a relationship between orthogonal vectors and the Cauchy-Riemann equations? And later again at timestamp 7:53 when I see the u1v1 + u2v2 = 0 equation, I'm reminded of some PDE's like Laplace's equation or something. is there a connection there that you are aware of? Perhaps between the concept of orthogonality and PDE's? if so, can you help me identify the connection or at least point me in the right direction so I can read about it or ponder it in more detail.

[@brightsideofmaths]

Thanks! Orthogonality is a very abstract concept with a lot of applications. You might be interested in my functional analysis series to see more: tbsom.de/s/fa

[@narendraparmar1631]

Thanks

[@brightsideofmaths]

No problem

[@wojciechnowacki1364]

Great video, thank you!

[@maxpercer7119]

2:00 superscripts instead of subscripts?

[@brightsideofmaths]

Yeah, an upper index to distinguish different vectors.

[@maxpercer7119]

@@brightsideofmaths interesting ;)

[@raunakmukherjee8029]

👍