Home/Algebra/Eigenvalues and diagonalization/Spectral theorem20. Eigenvalues and diagonalizationSpectral theoremLevel: avanzadoIn 20. Eigenvalues and diagonalizationFormulaCopy LaTeXA=AT⇒A=QΛQTA=A^T\Rightarrow A=Q\Lambda Q^TA=AT⇒A=QΛQTTagsalgebraeigenalgebra formulalinearvalues eigenDetailEvery real symmetric matrix admits an orthogonal diagonalization.Explore the ideaFound an error? Contact us.Related formulasRelatedSymmetric matrixAT=AA^T=AAT=AOpen formulaOpen in sectionRelatedOrthogonal matrixQTQ=I⇒Q−1=QTQ^TQ=I\Rightarrow Q^{-1}=Q^TQTQ=I⇒Q−1=QTOpen formulaOpen in sectionRelatedSpectral decompositionA=QΛQTA=Q\Lambda Q^TA=QΛQTOpen formulaOpen in section