Visualizing Diagonalization & Eigenbases
9:46
YouTubeDr. Trefor Bazett
Visualizing Diagonalization & Eigenbases
Diagonal transformations are really nice to visualize geometrically. In 2D they are just a combination of horizontal and vertical stretching. While a generic matrix isn't quite this nice, if you can find a basis of eigenvectors, then the transformation "looks" like stretching and compressing along those eigenvectors by the values of the ...
90.1K viewsJul 9, 2018
Diagonal Matrix Properties
Does the diagonal actually exist? 📐🤯 Imagine a perfectly square park, 100ft by 100ft. You need to get to the opposite corner. 🔹 Euclidean Math: Walk the diagonal = 141 ft. 🔹 Grid Rules: You can only move North or East. If you take the edge, it’s 200 ft. Too long. So you cut through the middle using stairs. 🪜 North, East, North, East. It looks shorter. So you shrink the stairs. You make them microscopic. You break the
2:00
Does the diagonal actually exist? 📐🤯 Imagine a perfectly square park, 100ft by 100ft. You need to get to the opposite corner. 🔹 Euclidean Math: Walk the diagonal = 141 ft. 🔹 Grid Rules: You can only move North or East. If you take the edge, it’s 200 ft. Too long. So you cut through the middle using stairs. 🪜 North, East, North, East. It looks shorter. So you shrink the stairs. You make them microscopic. You break the
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