characteristic polynomial

English

Noun

characteristic polynomial (plural characteristic polynomials)

1. (linear algebra) The determinant, of a matrix minus an indeterminant times the identity matrix

   The characteristic polynomial of $\left(\begin{array}{cc}1 & 4\\3 & -5\end{array}\right)$ is $\mathbf{Det}\left(\begin{array}{cc}1-x & 4\\ 3 & -5-x\end{array}\right)$.

Usage notes

Equally many authors instead subtract the matrix from the indeterminant times the identity matrix. But the result only differs by multiplication by -1, which isn't important where characteristic polynomials are studied.

Translations

linear algebra

• Estonian: karakteristlik polünoom (et)
• French: polynôme caractéristique (fr) m
• German: charakteristiches Polynom (de) n
• Hungarian: karakterisztikus polinom (hu)

• Portuguese: polinómio característico (pt) m, (Brazil) polinômio característico (pt) m
• Spanish: polinomio característico (es) m
• Swedish: karakteristiskt polynom (sv) n

See also

• minimal polynomial
• eigenvector
• eigenvalue