Full Example: Diagonalizing a Matrix
10:08
YouTubeDr. Trefor Bazett
Full Example: Diagonalizing a Matrix
Let's compute a full example of Diagonalizing a matrix via eigenvectors and eigenvalues. The steps: 1) Compute the eigenvalues. Take the determinant of A-lambda I and set it equal to zero. The solutions are the eigenvalues 2) Compute the eigenvectors. For each eigenvalue solve (A-lambda I)x=0, which is a homogeneous system 3) Form the P and D ...
622.3K views9 Jul 2017
Diagonal Matrix Properties
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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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