Home/Algebra/Eigenvalues and diagonalization/Eigenvalue equation20. Eigenvalues and diagonalizationEigenvalue equationLevel: intermedioIn 20. Eigenvalues and diagonalizationFormulaCopy LaTeXAv=λv,v≠0Av=\lambda v,\quad v\ne0Av=λv,v=0Tagsalgebraeigenalgebra formulalinearvalues eigenDetailAn eigenvector keeps its direction under A.Explore the ideaComputational complexityShow (CS mode)Found an error? Contact us.Related formulasRelatedCharacteristic equationdet(A−λI)=0\det(A-\lambda I)=0det(A−λI)=0Open formulaOpen in sectionRelatedDiagonalizationA=PDP−1A=PDP^{-1}A=PDP−1Open formulaOpen in section