4 ms·

3Blue1Brown has a good series on YouTube for building intuition in linear algebra: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab htt

3Blue1Brown has a good series on YouTube for building intuition in linear algebra: https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2x... In one of the last videos in the (relatively short) series, he discusses eigen-*: ~'eigen-stuffs are straight-forward but only make sense if you have a solid visual understanding of the pre-requisites (linear transformations, determinants, linear systems of equations, change of basis, etc.). Confusion about eigen-stuffs usually has more to do with a shaky foundation than the eigen-things themselves' https://youtu.be/PFDu9oVAE-g https://youtu.be/PFDu9oVAE-g All of the videos in the series, including this later one on eigen-things, focus on animations to show what the number crunching is doing to the coordinate system.

AceJohnny2 8y ago
3Blue1Brown (Grant Sanderson) is really, really good. I follow a number of education channels on YouTube, and Grant blows them all out of the water for the kind of insights, new perspectives, and inspiration he provides. His animations are fantastically put together to clearly and unobtrusively illustrate the point he's making. I also really like his voice, soothing, clear and with enough intonation to avoid boredom, and perfect pace. I wish I had his linear algebra series back in college, I suspect I would have done much better. He's the creator I support the most on Patreon: https://www.patreon.com/3blue1brown https://www.patreon.com/3blue1brown
- bashcorrupt 8y ago
  >I follow a number of education channels on YouTube Any recommendations? I would love to look into channels that you think are like 3Blue1Brown but in other subjects (natural sciences, history, art etc.).
  - AceJohnny2 8y ago
    Edit: I realize I overlooked the "like 3Blue1Brown" prereq, instead sharing a list of the educational/interesting channels I find worthwhile. The most like 3Blue1Brown will be the PBS ones (especially SpaceTime), MinutePhysics, and Mathologer, for using diagrams to convey abstract concepts. PBS Space Time and Eons are both awesome: * PBS Space Time, covers cosmology and quantum physics: https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g * PBS Eons, for geology and paleontology: https://www.youtube.com/channel/UCzR-rom72PHN9Zg7RML9EbA https://www.youtube.com/channel/UCzR-rom72PHN9Zg7RML9EbA * Smarter Every Day, Destin's enthusiasm is contagious: https://www.youtube.com/user/destinws2 https://www.youtube.com/user/destinws2 * Extra Credits various topics (video game design, History, and recently history of Sci-Fi) are great: https://www.youtube.com/user/ExtraCreditz https://www.youtube.com/user/ExtraCreditz * Today I Found Out is just on this side of clickbaity, and is this age's "Ripley's Believe It Or Not", but still interesting and more importantly well researched: https://www.youtube.com/user/TodayIFoundOut https://www.youtube.com/user/TodayIFoundOut * Crash Course, of course: https://www.youtube.com/channel/UCX6b17PVsYBQ0ip5gyeme-Q https://www.youtube.com/channel/UCX6b17PVsYBQ0ip5gyeme-Q * Gaming Historian, for some insight into the making of systems that formed my (and earlier) childhood: https://www.youtube.com/channel/UCnbvPS_rXp4PC21PG2k1UVg https://www.youtube.com/channel/UCnbvPS_rXp4PC21PG2k1UVg * Minute Physics, whose latest few videos made Special Relativity understandable to this peon: https://www.youtube.com/user/minutephysics/videos https://www.youtube.com/user/minutephysics/videos * Practical Engineering, for some insight into civil engineering topics that we take for granted: https://www.youtube.com/channel/UCMOqf8ab-42UUQIdVoKwjlQ https://www.youtube.com/channel/UCMOqf8ab-42UUQIdVoKwjlQ * Real Engineering, for insight into various other mechanical engineering topics: https://www.youtube.com/channel/UCR1IuLEqb6UEA_zQ81kwXfg https://www.youtube.com/channel/UCR1IuLEqb6UEA_zQ81kwXfg * Standup Maths, host Matt Parker was the first to make maths approachable for me again (before 3Blue1Brown took the lead): https://www.youtube.com/channel/UCSju5G2aFaWMqn-_0YBtq5A https://www.youtube.com/channel/UCSju5G2aFaWMqn-_0YBtq5A * Steve Mould, who covers various topics both mathematical and physical. You may have seen that gif of him demonstrating the "levitating" siphoning "pearl necklace" (also a friend of Matt Parker, above): https://www.youtube.com/channel/UCEIwxahdLz7bap-VDs9h35A https://www.youtube.com/channel/UCEIwxahdLz7bap-VDs9h35A * The 8-Bit Guy, for some history of early home computer systems: https://www.youtube.com/channel/UC8uT9cgJorJPWu7ITLGo9Ww https://www.youtube.com/channel/UC8uT9cgJorJPWu7ITLGo9Ww * Numberphile, the second-greatest math channel (after 3Blue1Brown), whose recent video finally made me take the Golden Ratio seriously, rather than an architectural gimmick/conspiracy theory: https://www.youtube.com/user/numberphile https://www.youtube.com/user/numberphile * Mathologer, another good math channel (but I must sheepishly admit I prefer 3Blue1Brown... sensing a pattern here?): https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg * Periodic Videos, for chemistry and physics, often featuring the iconic Dr Martyn Poliakoff: https://www.youtube.com/channel/UCtESv1e7ntJaLJYKIO1FoYw https://www.youtube.com/channel/UCtESv1e7ntJaLJYKIO1FoYw * NileRed, for some homegrown chemistry, I particularly appreciate the candor of the approach and results: https://www.youtube.com/user/TheRedNile https://www.youtube.com/user/TheRedNile Not quite as much "educational", but still very very good: * Every Frame A Painting, now finished, but a great explanation of what makes good cinematography: https://www.youtube.com/channel/UCjFqcJQXGZ6T6sxyFB-5i6A https://www.youtube.com/channel/UCjFqcJQXGZ6T6sxyFB-5i6A * NoClip, long-form documentaries about the making-of video games. Danny O'Dwyer is a treasure: https://www.youtube.com/channel/UC0fDG3byEcMtbOqPMymDNbw https://www.youtube.com/channel/UC0fDG3byEcMtbOqPMymDNbw Apologies for the link spam, this list turned out longer than I expected as I went down my subscriptions, and I've probably missed a few worthy ones! Edit the final: I discovered many of these channels through referrals from others I was watching, including from the twitter feeds of the authors. Turns out the educational landscape on YouTube is a well-connected graph!
    - emmelaich 8y ago
      Awesome but no Vsauce? https://www.youtube.com/channel/UC6nSFpj9HTCZ5t-N3Rm3-HA https://www.youtube.com/channel/UC6nSFpj9HTCZ5t-N3Rm3-HA
      - AceJohnny2 8y ago
        Y'know, I hesitated. I admit I'm somewhat ambivalent about VSauce, because Michael's somewhat wandering style makes it closer to entertainment than the usually more focused topics the other channels on my list work with. That said, Vsauce is definitely interesting and great for fostering curiosity and an inquisitive mindset. Also his new channel DONG ("Do Online Now Guys"... wut?): https://www.youtube.com/channel/UClq42foiSgl7sSpLupnugGA https://www.youtube.com/channel/UClq42foiSgl7sSpLupnugGA Also I should've mentioned Veritasium: https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA
    - Kagerjay 8y ago
      I just realized I had 80% of these subscribed already, then I looked at how many channels I subscribed too (700+) I like tinkering with things so I have some mechanical / electrical engineering / makers on my list as well. I listed my favorites of that list here * Tom Scott - Lots of interesting unique topics related to engineering, programming, and history https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A * Colin Furze - Lots of crazy welding projects https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A * Mark rober - ex-nasa engineer, similar to SmarterEveryDay https://www.youtube.com/channel/UCY1kMZp36IQSyNx_9h4mpCg https://www.youtube.com/channel/UCY1kMZp36IQSyNx_9h4mpCg * Hacksmith - just interesting project build videos normally related to marvel comics https://www.youtube.com/user/MstrJames https://www.youtube.com/user/MstrJames * Live overflow - web / binary hacking with great case studies https://www.youtube.com/channel/UClcE-kVhqyiHCcjYwcpfj9w https://www.youtube.com/channel/UClcE-kVhqyiHCcjYwcpfj9w * Wendover productions - Great documenatires on things like Airplane and shippping logistics https://www.youtube.com/wendoverproductions https://www.youtube.com/wendoverproductions * Strange parts - ex-programmer who sources components and parts overseas https://www.youtube.com/channel/UCO8DQrSp5yEP937qNqTooOw https://www.youtube.com/channel/UCO8DQrSp5yEP937qNqTooOw
- picklesman 8y ago
  I’ve taken 3 college level courses on linear algebra and only really got an intuition for eigenvectors/eigenvalues when watching his video series. Super great!
  - emmelaich 8y ago
    I had problems with Principal Component Analysis; nice to see he's got one on that as well! http://setosa.io/ev/principal-component-analysis/ http://setosa.io/ev/principal-component-analysis/ (edit: ugh, contains an ad for MacKeeper)
    - jjoonathan 8y ago
      What, you don't want to remove your mac from trash? Incidentally, that particular grammatical quirk is one I've seen a number of times. Is it a thing for people coming from Russian? Or just general difficulty with remembering the order of the two subjects in two-subject phrases?
smrq 8y ago
Just to throw in my own anecdote, I took linear algebra twice (in high school with no college credit, and in college) and I still couldn't ever remember afterwards what an eigenvector was until I watched that series. Now I'll probably never forget. He is an astonishing educator.
Kagerjay 8y ago
I just finished watching both his calculus series and linear algebra. I have to say 3blue1brown has made a mathematical masterpiece of a youtube series Neither of those subjects really clicked with me until I could visualize it in a 2D / 3D representation
bladecatcher 8y ago
It’s possible to understand eigen-* without having an understanding of determinants. That’s how they’re introduced in “Linear Algebra Done Right” - http://linear.axler.net/ http://linear.axler.net/
- tgb 8y ago
  And they exist in situations where determinants are difficult or impossible to define! Infinite dimensional vector spaces can still have transformations with eigenvectors but you generally can't define a determinant coherently for them (certainly they might have infinitely many eigenvalues and if the determinant is the product, then you have convergence problems). A classic example is that the standard Gaussian distribution is an eigenvector of the Fourier transform.
  - in9 8y ago
    You just blew my mind with this comment. I'm a statistics undergrad student and I really need to up my math knowledge. Where is this fact from? Functional analysis?
    - tgb 8y ago
      Yeah that would be a good course to learn it - functional analysis is basically linear algebra on infinite dimensional vector spaces. (Though that sells it a little short - moving to infinite dimensional vector spaces requires incorporating some topology too.)

AceJohnny2 8y ago

3Blue1Brown (Grant Sanderson) is really, really good. I follow a number of education channels on YouTube, and Grant blows them all out of the water for the kind of insights, new perspectives, and inspiration he provides. His animations are fantastically put together to clearly and unobtrusively illustrate the point he's making. I also really like his voice, soothing, clear and with enough intonation to avoid boredom, and perfect pace. I wish I had his linear algebra series back in college, I suspect I would have done much better. He's the creator I support the most on Patreon: https://www.patreon.com/3blue1brown https://www.patreon.com/3blue1brown

bashcorrupt 8y ago
>I follow a number of education channels on YouTube Any recommendations? I would love to look into channels that you think are like 3Blue1Brown but in other subjects (natural sciences, history, art etc.).
- AceJohnny2 8y ago
  Edit: I realize I overlooked the "like 3Blue1Brown" prereq, instead sharing a list of the educational/interesting channels I find worthwhile. The most like 3Blue1Brown will be the PBS ones (especially SpaceTime), MinutePhysics, and Mathologer, for using diagrams to convey abstract concepts. PBS Space Time and Eons are both awesome: * PBS Space Time, covers cosmology and quantum physics: https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g https://www.youtube.com/channel/UC7_gcs09iThXybpVgjHZ_7g * PBS Eons, for geology and paleontology: https://www.youtube.com/channel/UCzR-rom72PHN9Zg7RML9EbA https://www.youtube.com/channel/UCzR-rom72PHN9Zg7RML9EbA * Smarter Every Day, Destin's enthusiasm is contagious: https://www.youtube.com/user/destinws2 https://www.youtube.com/user/destinws2 * Extra Credits various topics (video game design, History, and recently history of Sci-Fi) are great: https://www.youtube.com/user/ExtraCreditz https://www.youtube.com/user/ExtraCreditz * Today I Found Out is just on this side of clickbaity, and is this age's "Ripley's Believe It Or Not", but still interesting and more importantly well researched: https://www.youtube.com/user/TodayIFoundOut https://www.youtube.com/user/TodayIFoundOut * Crash Course, of course: https://www.youtube.com/channel/UCX6b17PVsYBQ0ip5gyeme-Q https://www.youtube.com/channel/UCX6b17PVsYBQ0ip5gyeme-Q * Gaming Historian, for some insight into the making of systems that formed my (and earlier) childhood: https://www.youtube.com/channel/UCnbvPS_rXp4PC21PG2k1UVg https://www.youtube.com/channel/UCnbvPS_rXp4PC21PG2k1UVg * Minute Physics, whose latest few videos made Special Relativity understandable to this peon: https://www.youtube.com/user/minutephysics/videos https://www.youtube.com/user/minutephysics/videos * Practical Engineering, for some insight into civil engineering topics that we take for granted: https://www.youtube.com/channel/UCMOqf8ab-42UUQIdVoKwjlQ https://www.youtube.com/channel/UCMOqf8ab-42UUQIdVoKwjlQ * Real Engineering, for insight into various other mechanical engineering topics: https://www.youtube.com/channel/UCR1IuLEqb6UEA_zQ81kwXfg https://www.youtube.com/channel/UCR1IuLEqb6UEA_zQ81kwXfg * Standup Maths, host Matt Parker was the first to make maths approachable for me again (before 3Blue1Brown took the lead): https://www.youtube.com/channel/UCSju5G2aFaWMqn-_0YBtq5A https://www.youtube.com/channel/UCSju5G2aFaWMqn-_0YBtq5A * Steve Mould, who covers various topics both mathematical and physical. You may have seen that gif of him demonstrating the "levitating" siphoning "pearl necklace" (also a friend of Matt Parker, above): https://www.youtube.com/channel/UCEIwxahdLz7bap-VDs9h35A https://www.youtube.com/channel/UCEIwxahdLz7bap-VDs9h35A * The 8-Bit Guy, for some history of early home computer systems: https://www.youtube.com/channel/UC8uT9cgJorJPWu7ITLGo9Ww https://www.youtube.com/channel/UC8uT9cgJorJPWu7ITLGo9Ww * Numberphile, the second-greatest math channel (after 3Blue1Brown), whose recent video finally made me take the Golden Ratio seriously, rather than an architectural gimmick/conspiracy theory: https://www.youtube.com/user/numberphile https://www.youtube.com/user/numberphile * Mathologer, another good math channel (but I must sheepishly admit I prefer 3Blue1Brown... sensing a pattern here?): https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg * Periodic Videos, for chemistry and physics, often featuring the iconic Dr Martyn Poliakoff: https://www.youtube.com/channel/UCtESv1e7ntJaLJYKIO1FoYw https://www.youtube.com/channel/UCtESv1e7ntJaLJYKIO1FoYw * NileRed, for some homegrown chemistry, I particularly appreciate the candor of the approach and results: https://www.youtube.com/user/TheRedNile https://www.youtube.com/user/TheRedNile Not quite as much "educational", but still very very good: * Every Frame A Painting, now finished, but a great explanation of what makes good cinematography: https://www.youtube.com/channel/UCjFqcJQXGZ6T6sxyFB-5i6A https://www.youtube.com/channel/UCjFqcJQXGZ6T6sxyFB-5i6A * NoClip, long-form documentaries about the making-of video games. Danny O'Dwyer is a treasure: https://www.youtube.com/channel/UC0fDG3byEcMtbOqPMymDNbw https://www.youtube.com/channel/UC0fDG3byEcMtbOqPMymDNbw Apologies for the link spam, this list turned out longer than I expected as I went down my subscriptions, and I've probably missed a few worthy ones! Edit the final: I discovered many of these channels through referrals from others I was watching, including from the twitter feeds of the authors. Turns out the educational landscape on YouTube is a well-connected graph!
  - emmelaich 8y ago
    Awesome but no Vsauce? https://www.youtube.com/channel/UC6nSFpj9HTCZ5t-N3Rm3-HA https://www.youtube.com/channel/UC6nSFpj9HTCZ5t-N3Rm3-HA
    - AceJohnny2 8y ago
      Y'know, I hesitated. I admit I'm somewhat ambivalent about VSauce, because Michael's somewhat wandering style makes it closer to entertainment than the usually more focused topics the other channels on my list work with. That said, Vsauce is definitely interesting and great for fostering curiosity and an inquisitive mindset. Also his new channel DONG ("Do Online Now Guys"... wut?): https://www.youtube.com/channel/UClq42foiSgl7sSpLupnugGA https://www.youtube.com/channel/UClq42foiSgl7sSpLupnugGA Also I should've mentioned Veritasium: https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA https://www.youtube.com/channel/UCHnyfMqiRRG1u-2MsSQLbXA
  - Kagerjay 8y ago
    I just realized I had 80% of these subscribed already, then I looked at how many channels I subscribed too (700+) I like tinkering with things so I have some mechanical / electrical engineering / makers on my list as well. I listed my favorites of that list here * Tom Scott - Lots of interesting unique topics related to engineering, programming, and history https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A * Colin Furze - Lots of crazy welding projects https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A https://www.youtube.com/channel/UCBa659QWEk1AI4Tg--mrJ2A * Mark rober - ex-nasa engineer, similar to SmarterEveryDay https://www.youtube.com/channel/UCY1kMZp36IQSyNx_9h4mpCg https://www.youtube.com/channel/UCY1kMZp36IQSyNx_9h4mpCg * Hacksmith - just interesting project build videos normally related to marvel comics https://www.youtube.com/user/MstrJames https://www.youtube.com/user/MstrJames * Live overflow - web / binary hacking with great case studies https://www.youtube.com/channel/UClcE-kVhqyiHCcjYwcpfj9w https://www.youtube.com/channel/UClcE-kVhqyiHCcjYwcpfj9w * Wendover productions - Great documenatires on things like Airplane and shippping logistics https://www.youtube.com/wendoverproductions https://www.youtube.com/wendoverproductions * Strange parts - ex-programmer who sources components and parts overseas https://www.youtube.com/channel/UCO8DQrSp5yEP937qNqTooOw https://www.youtube.com/channel/UCO8DQrSp5yEP937qNqTooOw
picklesman 8y ago
I’ve taken 3 college level courses on linear algebra and only really got an intuition for eigenvectors/eigenvalues when watching his video series. Super great!
- emmelaich 8y ago
  I had problems with Principal Component Analysis; nice to see he's got one on that as well! http://setosa.io/ev/principal-component-analysis/ http://setosa.io/ev/principal-component-analysis/ (edit: ugh, contains an ad for MacKeeper)
  - jjoonathan 8y ago
    What, you don't want to remove your mac from trash? Incidentally, that particular grammatical quirk is one I've seen a number of times. Is it a thing for people coming from Russian? Or just general difficulty with remembering the order of the two subjects in two-subject phrases?

smrq 8y ago

Just to throw in my own anecdote, I took linear algebra twice (in high school with no college credit, and in college) and I still couldn't ever remember afterwards what an eigenvector was until I watched that series. Now I'll probably never forget. He is an astonishing educator.

Kagerjay 8y ago

I just finished watching both his calculus series and linear algebra. I have to say 3blue1brown has made a mathematical masterpiece of a youtube series Neither of those subjects really clicked with me until I could visualize it in a 2D / 3D representation

bladecatcher 8y ago

It’s possible to understand eigen-* without having an understanding of determinants. That’s how they’re introduced in “Linear Algebra Done Right” - http://linear.axler.net/ http://linear.axler.net/

tgb 8y ago
And they exist in situations where determinants are difficult or impossible to define! Infinite dimensional vector spaces can still have transformations with eigenvectors but you generally can't define a determinant coherently for them (certainly they might have infinitely many eigenvalues and if the determinant is the product, then you have convergence problems). A classic example is that the standard Gaussian distribution is an eigenvector of the Fourier transform.
- in9 8y ago
  You just blew my mind with this comment. I'm a statistics undergrad student and I really need to up my math knowledge. Where is this fact from? Functional analysis?
  - tgb 8y ago
    Yeah that would be a good course to learn it - functional analysis is basically linear algebra on infinite dimensional vector spaces. (Though that sells it a little short - moving to infinite dimensional vector spaces requires incorporating some topology too.)