##  [Characteristic Polynomial](/characteristic-polynomial) 

  ##  [Characteristic Polynomial](https://natural.quantumdictionary.io/characteristic-polynomial-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For a square linear operator or matrix A, the polynomial p_A(λ) = det(A - λI) whose roots are the scalar parameters for which A - λI is singular.

 

 

 

 

 





 

 



 ##  [Characteristic Polynomial](https://algebra.quantumdictionary.io/characteristic-polynomial-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

For an n×n matrix A or linear operator, the characteristic polynomial is the monic polynomial p(λ)=det(λI−A) whose roots are the eigenvalues of A (over an algebraic closure), with multiplicities equal to algebraic multiplicities.