characteristic polynomial
Noun
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Noun
characteristic polynomial (plural characteristic polynomials)
- (linear algebra) The polynomial produced from a given square matrix by first subtracting the appropriate identity matrix multiplied by an indeterminant and then calculating the determinant.
- The characteristic polynomial of \textstyle\left(\begin{array}{cc}1 & 4\\3 & -5\end{array}\right) is \textstyle\left\vert\begin{array}{cc}1-x & 4\\ 3 & -5-x\end{array}\right\vert=x^2+4x-17.
- The characteristic polynomial of a 2 \times 2 matrix M is \lambda^2 - \mbox{tr}(M) \lambda + \mbox{det} (M), where \mbox{tr}(M) denotes the trace of M and \mbox{det}(M) denotes the determinant of M.
- The characteristic polynomial of a 3 \times 3 matrix M is -\lambda^3 + \mbox{tr}(M)\lambda^2 - \mbox{tr}(\mbox{adj}(M))\lambda + \mbox{det}(M), where \mbox{adj}(M) denotes the adjugate of M.
- (mathematics) A polynomial P(r) corresponding to a homogeneous, linear, ordinary differential equation P(D) y = 0 where D is a differential operator (with respect to a variable t, if y is a function of t).
- characteristic equation
- characteristic root
- characteristic vector
- French: polynôme caractéristique
- German: charakteristiches Polynom
- Italian: polinomio caratteristico
- Portuguese: polinómio característico, (Brazil) polinômio característico
- Spanish: polinomio característico
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003