Is a matrix diagonalizable, if one of its eigenvalues is zero?

$D$ is a diagonal matrix. A square matrix is a diagonal matrix if and only if the off-diagonal entries are $0$.

Hence your matrix is diagonalizable.

In fact, if the eigenvalues are all distinct, then it is diagonalizable.


Every Matrix is diagonalisable if it's eigenvalues are all distinct, no matter the values of the eigenvalue theirselves. Also your second Matrix is diagonal, cause you only have terms on the diagonal, respectively 0, 4 and 12.

Tags:

Linear Algebra

Eigenvalues Eigenvectors

Diagonalization

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