Uploaded January 2022 | Updated September 2026, 1 week ago
An explanation of why a function has at most one two-sided inverse. To prove this result, we prove that an injective function has at most one right inverse.
Functions playlist: youtube.com/playlist?list=PLug5ZIRrShJG35bSmijiKFxerMar8jMCi
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Music: OcularNebula - The Lopez
An explanation of why a function has at most one two-sided inverse. To prove this result, we prove that an injective function has at most one right inverse.
Functions playlist: youtube.com/playlist?list=PLug5ZIRrShJG35bSmijiKFxerMar8jMCi
Subscribe to see more new math videos!
Music: OcularNebula - The Lopez
![How the Matrix Characteristic Polynomial is Connected to F[x]-Modules](https://i.ytimg.com/vi/jCt6mR3QtPk/mqdefault.jpg "How the Matrix Characteristic Polynomial is Connected to F[x]-Modules
Rational canonical form: https://youtu.be/q5uj4o0O5R0
Similar matrices isomorphism: https://youtu.be/-ligAAxFM8Y
Intro to F[x]-modules: https://youtu.be/H44q_Urmts0
The characteristic polynomial described by the determinant det(xI-A) is very useful when studying matrices. It turns out that its related to modules as well! Here we show how the characteristic polynomial is related to the module form of an arbitrary matrix.
Ring & Module Theory playlist: https://www.youtube.com/playlist?list=PLug5ZIRrShJExMapwnaKTFXDYbKeWDXq7
0:00 Computing the determinant
10:07 Similar matrices have same polynomial
12:40 Proof for a general matrix
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Music: C418 - Pr Department")
