The Tensor Confusion: Why So Many Definitions?

Comments · 23

• MI

  @MinhAnh-n1w-h9b · 2 weeks ago

  The best explanation of tensor

• SE

  @Sergio_M97 · 1 month ago

  A tensor can be understood as a multilinear function, an element of a tensor product, or a multidimensional array, due to the isomorphisms between these spaces. This is precisely why the tensor product is ultimately defined through its universal property.

  1

• RI

  @Rick-h4q9s · 1 month ago

  Great vid. Is it possible to get one on tensor products?

  1

• HA

  @harrywoodell7008 · 2 weeks ago

  I walk up a hill, and as the crow flies, I walked way more.  The metric tensor.  Want skew with that?  Walk a back and forth path up a hill to keep the slope and grip on the surface manageable.  So we get skew.  Walking in Appalachia is a metric tensor.  QED.

• DR

  @DR-tx3ix · 3 weeks ago

  The first half was fine, I could follow along keeping the (x,y) basis vs (r, theta) basis in mind. But after around <a href="https://www.youtube.com/watch?v=apVssMMfYpY&amp;t=1260">21:00</a> it became mostly textbook equations. (nothing wrong with that but it didn&apos;t do me any good).

• FA

  @fabiobrainer573 · 4 days ago

  Em alguns casos se pode dizer que vetores são tensores e tensores são vetores, se colocados juntos, isso parece não fazer sentido

• FA

  @fabiobrainer573 · 4 days ago (edited)

  Eu: venho pela definição formal matemática <br>Ele: &quot;vou ignorar a definição formal neste vídeo!&quot; <br>🤨 Estou sendo sabotado...

• TO

  @TonyIta-w1p · 1 month ago

  ALL THREE DEFINITIONS ARE RIGHT, IF YOU KNOW THAT A JACOBIAN IS ANOTHER NAME FOR A MULTILINEAR MAP AND A MULTILINEAR MAP IS JUST ANOTHER NAME FOR A MULTIPLE ARRAY. THE DIMENSIONS OF THE JACOBIAN = SAME DIMENSION OF THE MULTILINEAR MAP = SAME DIMENSION OF THE MULTIPLE ARRAY. &nbsp;THEY ARE POINTING TO THE EXACT SAME PHYSICAL OBJECT IN A GIVEN-DIMENSIONAL HILBERT SPACE. THE PHYSICISTS OFTEN STOP AT FOUR DIMENSIONS, WHILST THE COMPUTER SCIENTISTS &amp; MATHEMATICIANS MAY DEAL WITH TENSORS OF ANY DIMENSIONS. THE EXPRESSIVE POWER OF TENSORS IN COMPUTATION IS PHENOMENAL. E.G. COMPUTER GAMES &amp; LLMs.

  1

• FR

  @Fritzbedeek · 2 months ago

  ...or as Kip Thorne describes them:<br>A box with slots into which you put vectors and it spits out a real number...<br><br><a href="https://www.youtube.com/watch?v=9ke9rHq22kg&amp;list=PLaLOVNqqD-2H-fiiL5Lxmmuhquem-zNIC">https://m.youtube.com/watch?v=9ke9rHq22kg&amp;list=PLaLOVNqqD-2H-fiiL5Lxmmuhquem-zNIC&amp;index=5&amp;pp=iAQB</a>

  1

• LA

  @lazylazibandi · 2 months ago

  There is a language abuse by the CS and nothing more.