Home/Algebra/Eigenvalues and diagonalization/Characteristic equation20. Eigenvalues and diagonalizationCharacteristic equationLevel: intermedioIn 20. Eigenvalues and diagonalizationFormulaCopy LaTeXdet(A−λI)=0\det(A-\lambda I)=0det(A−λI)=0Tagsalgebraeigenalgebra formulalinearvalues eigenDetailIts roots are the eigenvalues.Explore the ideaFound an error? Contact us.Related formulasRelatedEigenvalue equationAv=λv,v≠0Av=\lambda v,\quad v\ne0Av=λv,v=0Open formulaOpen in sectionRelatedFactorization by rootsP(x)=an∏k=1n(x−rk)P(x)=a_n\prod_{k=1}^{n}(x-r_k)P(x)=ank=1∏n(x−rk)Open formulaOpen in section