Business I / Matrix Diagonalisation
Practice question · Put in order

Order the diagonalisation procedure.

Hints
  1. The eigenvalues must be found before their directions.
  2. The decomposition is assembled last.
Show the answer
  1. Find eigenvalues: solve det⁡(A−λI)=0\det(A - \lambda I) = 0
  2. Find eigenvectors: solve (A−λI)v=0(A - \lambda I)\mathbf{v} = \mathbf{0}
  3. Form PP from eigenvector columns
  4. Form DD with eigenvalues on diagonal
  5. Verify A=PDP−1A = PDP^{-1}
Why

Eigenvalues first (characteristic equation), then eigenvectors (null space), then assemble the decomposition.

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