📘 What are Eigenvalues & Eigenvectors?
In linear algebra, eigenvectors are special vectors whose direction remains unchanged under a given linear transformation. The factor by which they stretch is the eigenvalue.
Mathematically, for a matrix A and vector v:
A · v = λ · v
This means applying matrix A to vector v simply scales v by λ.
Applications: PCA, Markov chains, quantum mechanics, facial recognition, vibration modes.
🌀 Visualizing Matrix Action
🧊 2×2 Eigenvalue Calculator
Enter a 2×2 matrix to compute eigenvalues:
A·v = λ·v
∇²φ = 0
ψ(x) = Aei(kx−ωt)
∑ₙ=1^∞ 1/n² = π²/6
∂²u/∂t² = c²∇²u
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A·v = λ·v
∇²φ = 0
ψ(x) = Aei(kx−ωt)
∑ₙ=1^∞ 1/n² = π²/6
∂²u/∂t² = c²∇²u