MathLiveCayley–Hamilton theorem
A square matrix substituted into its own characteristic polynomial gives the zero matrix. It is used to simplify matrix powers and inverses and in linear algebra proofs.
p_A(A)=0What the symbols mean
| a square matrix | |
| the characteristic polynomial of A, p_A(\lambda)=\det(\lambda I - A) |
About this formula
- FieldMathematics
- TopicLinear algebra
- LevelUniversity
- Also calledCayley-Hamilton theorem, Cayley-Hamilton, matrix satisfies its characteristic equation, characteristic polynomial annihilates matrix, square matrix characteristic equation
- SourceWikidata Q656772
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