A-Level Further Maths · Further Pure
Eigenvectors
What is it
An eigenvector is the specific direction (vector) that a matrix transformation stretches without rotating, corresponding to a particular eigenvalue — found by solving (A - λI)v = 0 for each eigenvalue λ.
Why it matters
Eigenvectors and eigenvalues together fully describe how a matrix transformation behaves, and this pairing is the mathematical foundation behind Google's original PageRank algorithm, structural engineering analysis, and image compression.
Exam tip
After finding an eigenvector, double-check it by multiplying it by the original matrix and confirming the result is the eigenvector scaled by its eigenvalue — this verification step catches most eigenvector calculation errors immediately.
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