CS223 · Annotated SlidesChapter 5 — The Characteristic Equation
Chapter 5 · Annotated slides

The Characteristic Equation

Determinants recalled, the characteristic equation det(A − λI) = 0, algebraic multiplicity, and similar matrices.

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Slide 1: Recalling some concepts
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      1. λ is an eigenvalue ⇔ det(A − λI) = 0 (the characteristic equation). Multiplicity as a root = algebraic multiplicity.
      🎯 How this can come up · 1 question
      Written

      Find the eigenvalues of A = [[2, 3], [3, −6]].

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          1. Similar matrices (B = P⁻¹AP) have the same characteristic polynomial, hence the same eigenvalues.
          Exam trapSame eigenvalues does NOT imply similar; row-equivalent matrices usually have different eigenvalues.
          Slide 7: Example:
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