Uploaded October 2024 | Updated September 2026, 1 week ago
Upper triangular matrices video: youtu.be/p0_3BDvf9JA
Did you know about this very nice equation with the matrix exponential? In this video we prove the result by reducing to the upper triangular case and connect it to basic identities of the exponential function.
Learning Linear Algebra playlist: youtube.com/playlist?list=PLug5ZIRrShJHNCfEiX6l5CKbljWayGEcs
0:00 Reducing to Upper Triangular
8:53 Main Proof
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Music: C418 - Smooth Fall
Upper triangular matrices video: youtu.be/p0_3BDvf9JA
Did you know about this very nice equation with the matrix exponential? In this video we prove the result by reducing to the upper triangular case and connect it to basic identities of the exponential function.
Learning Linear Algebra playlist: youtube.com/playlist?list=PLug5ZIRrShJHNCfEiX6l5CKbljWayGEcs
0:00 Reducing to Upper Triangular
8:53 Main Proof
Subscribe to see more new math videos!
Music: C418 - Smooth Fall
![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")
