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AI & Machine Learning Worksheet
🤖 Eigenvalues & Eigenvectors
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Intuit Av = lambda vDirections that only scaleWhy PCA uses themFind simple eigenvalues📚 Quick Recap
"Eigenvalues and eigenvectors" sounds like the scariest part of linear algebra, and a lot of courses introduce it with dense proofs that make it feel that way. The actual idea is simpler than the name suggests: when a matrix transforms a vector, most vectors get both stretched and rotated — but a special few only get stretched, never rotated. Those special directions are eigenvectors, and how much they get stretched is the eigenvalue.
🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1An eigenvector under A only gets:
2The scale factor is the:
3Eigen-analysis powers which ML technique?
4Eigenvalues of a diagonal matrix are:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5The defining equation: A v = v.
6Eigenvectors keep their under the transform.
7Eigenvalues of [[3,0],[0,7]]?
8Why does PCA pick top eigenvectors?
9Geometric meaning of lambda = 1?
🚀 Section C · Challenge ● CHALLENGE 5
10What does a negative eigenvalue do?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 lambda 6 direction 7 = 3 and 7 (diagonal) 8 = They are the directions of maximum variance in the data 9 = That direction is unchanged in length | 10 = Flips the direction while scaling