What is it
Undergraduate treatment of eigenvalues extends A-Level Further Maths work to diagonalisation — expressing a matrix in terms of its eigenvalues and eigenvectors to dramatically simplify calculations like computing high powers of a matrix.
Why it matters
Diagonalisation via eigenvalues is what makes many otherwise intractable calculations feasible — calculating A¹⁰⁰ directly is impractical, but becomes trivial once A is diagonalised, a technique used throughout applied mathematics and data science.
Exam tip
Before attempting to diagonalise a matrix, check that it has enough linearly independent eigenvectors to match its size — a matrix with repeated eigenvalues doesn't always diagonalise, and spotting this early avoids wasted work.
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