A-Level Further Maths · Further Pure
Eigenvalues
What is it
An eigenvalue is a scalar λ such that a matrix transformation stretches (but doesn't rotate) a specific vector by that factor — found by solving the characteristic equation det(A - λI) = 0.
Why it matters
Eigenvalues reveal the fundamental 'stretching directions' hidden within a matrix transformation, a concept used throughout engineering (vibration analysis), data science (principal component analysis), and quantum mechanics.
Exam tip
Expand the determinant of (A - λI) carefully and methodically — a single sign error here makes the entire characteristic equation wrong, and it's the most common source of mistakes in eigenvalue problems.
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