Linear Decomposition by the Dot Product

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  • Опубліковано 24 гру 2024

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  • @johnathancorgan3994
    @johnathancorgan3994 6 місяців тому +6

    After decades of using linear algebra in professional work, I still find these treatments of the basics quite refreshing and sometimes even enlightening. There is an elegance to the part of the world that can be modeled and predicted by linear maps.

  • @SimchaWaldman
    @SimchaWaldman 6 місяців тому +3

    In the thumbnail, you can use LaTeX coding *\imath* and *\jmath* to get a dotless *i* and *j* respectively.

    • @MathTheBeautiful
      @MathTheBeautiful  6 місяців тому +2

      Thank you! Yes, I think that would have been better!

  • @Fractured_Scholar
    @Fractured_Scholar 4 місяці тому +1

    Earlier in the series you mentioned that some of the geometry problems "become a joke" when we start solving solving them with vectors. Can we expect examples of that in the near future?

    • @MathTheBeautiful
      @MathTheBeautiful  4 місяці тому

      There are some in the past! This and the following four videos: ua-cam.com/video/erqHJeEsMPc/v-deo.html

    • @Fractured_Scholar
      @Fractured_Scholar 4 місяці тому

      @@MathTheBeautiful - Thank you kindly, sir.

  • @ralvarezb78
    @ralvarezb78 6 місяців тому

    Very clear and impressive MASTERCLASS

    • @MathTheBeautiful
      @MathTheBeautiful  6 місяців тому +1

      Thank you!

    • @ralvarezb78
      @ralvarezb78 6 місяців тому +1

      ​@@MathTheBeautifulThanks to you. I'm electrical engineer, with more than 15 years of experience and I'll subscribe next Monday on Maths at "Université de la Sorbonne" (Paris). Your video transmits not only deep knowledge on what is going on, but also passion of the teacher, and this is the very important thing. Congratulations!

  • @wagsman9999
    @wagsman9999 6 місяців тому

    Gorgeous stuff.

  • @kingplunger1
    @kingplunger1 5 місяців тому

    This is not the end yet, is it ? Nevermind: You just uploaded again :)

  • @FranzBiscuit
    @FranzBiscuit 6 місяців тому

    Well done, I think I actually get it now! The presentation was wonderful, very enjoyable indeed. Cheers.
    SUBSCRIBED

  • @tomholroyd7519
    @tomholroyd7519 6 місяців тому

    oh did you mention to your students the identity matrix hidden in the metric? 'cuz you know

  • @tomholroyd7519
    @tomholroyd7519 6 місяців тому

    Ooooh Kayyyy Gram Matrix from now on

  • @joeheafner2495
    @joeheafner2495 6 місяців тому +2

    BOOM! This may very well be the best way to bring the metric tensor into introductory physics.

  • @Pluralist
    @Pluralist 6 місяців тому