##  [Algebraic Multiplicity](/algebraic-multiplicity) 

  ##  [Algebraic Multiplicity](https://mathlogic.quantumdictionary.io/algebraic-multiplicity-0) 

  

 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural & Formal Sciences -

**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The algebraic multiplicity of an eigenvalue is the multiplicity of that scalar as a root of the characteristic polynomial of a linear operator or matrix; it counts how many times the eigenvalue appears as a factor (λ − λ0) in the characteristic polynomial.

 

 

 

 

 





 

 



 ##  [Algebraic Multiplicity](https://algebra.quantumdictionary.io/algebraic-multiplicity-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

The exponent of an eigenvalue as a root of the characteristic polynomial of a linear operator or matrix; equivalently, the power of the corresponding linear factor in the polynomial factorization.