Uploaded January 2020 | Updated September 2026, 1 week ago
Video on the dot product: youtu.be/y-kafkvDkFg
Cross product: youtu.be/RecUff64IX0
Differentiating dot products and cross products gives a surprisingly simple formula. But why is that formula so simple? It's time to break down the components of each product!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
New math videos every Monday and Friday. Subscribe to make sure you see them!
Video on the dot product: youtu.be/y-kafkvDkFg
Cross product: youtu.be/RecUff64IX0
Differentiating dot products and cross products gives a surprisingly simple formula. But why is that formula so simple? It's time to break down the components of each product!
Full Valuable Vector Calculus playlist: youtube.com/playlist?list=PLug5ZIRrShJHgsWPng59fFFoqn183aO-1
New math videos every Monday and Friday. Subscribe to make sure you see them!
![Matrix Invertibility With F[x]-Modules](https://i.ytimg.com/vi/xnZ2d6y8JmA/mqdefault.jpg "Matrix Invertibility With F[x]-Modules
Characteristic polynomial explanation: https://youtu.be/jCt6mR3QtPk
Ring & Module Theory playlist: https://youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFXDYbKeWDXq7
In this video, we use F[x]-modules to prove that a matrix is invertible if and only if its determinant is nonzero. Another example of how F[x]-modules can be applied to a ton of things in linear algebra!
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Music: OcularNebula - The Lopez")
