Uploaded November 2021 | Updated September 2026, 1 week ago
In this video, I prove two linear algebra facts with an almost identical proof! First, I show that every linear transformation from a finite dimensional vector space to itself must be bounded. Then I show that any two norms on a finite dimensional vector space are equivalent!
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In this video, I prove two linear algebra facts with an almost identical proof! First, I show that every linear transformation from a finite dimensional vector space to itself must be bounded. Then I show that any two norms on a finite dimensional vector space are equivalent!
YouTube channel: youtube.com/drpeyam
TikTok: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam








![e to a matrix
e to a matrix
You probably know about e to a number, but did you know you can calculate e to a matrix? We use eigenvalues and eigenvectors to calculate the matrix exponential e to the [-2 2;6 5]. In a later video (see Systems of ODE playlist) we can use that to solve the system of ODE x = Ax. Enjoy!
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