Business I / Eigenvalues and Eigenvectors
Practice question · Match the pairs

Match each object to its role.

  • Eigenvector
  • Eigenvalue
  • Characteristic polynomial
  • Eigenspace
  • det(AλI)\det(A - \lambda I), whose roots are the λ\lambdas
  • Direction the matrix only scales
  • The scaling factor on that direction
  • All eigenvectors sharing one λ\lambda
Hints
  1. Separate the direction from the factor from the equation that finds them.
  2. One object is the whole family sharing a single factor.
Show the answer
  • Eigenvector Direction the matrix only scales
  • Eigenvalue The scaling factor on that direction
  • Characteristic polynomial det(AλI)\det(A - \lambda I), whose roots are the λ\lambdas
  • Eigenspace All eigenvectors sharing one λ\lambda
Why

Direction, factor, detector, and family, the four nouns of eigen-theory.

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