NETMaths
Log inStart free

Is this true?

A real matrix with all real eigenvalues is orthogonally diagonalisable

No — it is false.

The counterexample

[[1,1],[0,1]]

Eigenvalue 1 twice but only one eigenvector; orthogonal diagonalisability requires symmetry.

The kind of mistake this is

Converse assumed

The theorem runs one way. You used it in the other.

Drill statements like this
linear algebra

Others that fail the same way

From Inner Product Spaces and Forms › Gram–Schmidt, orthogonal/unitary/normal matrices, spectral theorem

ShareWhatsAppTelegram