A Number to the Power of a Matrix - Numberphile

Comments · 511

• TO

  @TomRocksMaths · 1 year ago

  Coming soon - a number to the power of an operator... oh hello Quantum Mechanics.

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• GA

  @Galva94a · 1 year ago (edited)

  I think Tom missed a great opportunity for talking about how COMPLEX NUMBERS could be represented with matrices (where the imaginary unit &quot;i&quot; is the matrix (0,-1,1,0)<br><br>The formula then becomes euler&apos;s formula: e^iwt=cos(wt) + i sin(wt)

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• GO

  @gowzahr · 1 year ago

  You know he&apos;s a real mathematician because when asked about the &apos;t&apos;, he didn&apos;t talk about any of the real world applications, he instead took the opportunity to talk about more math.

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• OH

  @ohadcohen9813 · 1 year ago

  I was missing the explanation that this is the &apos;rotation operator&apos;. This links to many results in physics where either a vector is rotated about the origin, or a mass oscilates with a fixed frequency &apos;w&apos;.

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• DA

  @davidiverson5928 · 1 year ago

  &quot;Why the tea?&quot; &nbsp;British people always need tea.

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• DI

  @dikkedorus · 1 year ago

  The thing that I was missing is that the matrix you get is actually the 2D rotation matrix of omega degrees. As a graphics programmer I recognized it pretty early on and I thought that that was where it was going. Effectively you can multiply a vector with that matrix to rotate it along Origin; this is used extensively in 3D computer graphics and animation. It was probably the first matrix I learned doodling away as a teenager.

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• RE

  @regulus2033 · 1 year ago

  <a href="https://www.youtube.com/watch?v=CHozRTwHInE&amp;t=735">12:15</a> &quot;It doesn&apos;t have a nice name&quot;<br>Pauli: &quot;Am I a joke to you????&quot;

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• JE

  @JesseHersch · 1 year ago

  I remember this from quantum mechanics! Seemed crazy at the time but you get used to it. Like that von Neumann quote: &quot;in mathematics you don&apos;t understand things. You just get used to them&quot;<br><br>I think he understood them though.

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• RA

  @radiac6818 · 1 year ago

  Rumor has it that famed theoretical physicist Paul A. M. Dirac first figured this out, in his head, while attending a cocktail party.

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• JA

  @Jackal_Anubis · 1 year ago

  Not factoring out the omega for so long was diabolical, it had me on the edge of my seat.

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• ER

  @ErikScott128 · 1 year ago

  This is the beginning of linear multi-variable differential equations. In practice, you never actually have to do any of this math again once you&apos;ve proven it, but it&apos;s still important. Steve Brunton here on YouTube has some excellent lectures on this stuff, and it&apos;s honestly a much better introduction to differential equations than what I had in undergrad.

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• YO

  @youneskafie2008 · 1 year ago

  OMG this was crazy, really nice &nbsp;when you can go from linear algebra to calculus without expecting it.

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