# Symmetric matrix is always diagonalizable?

I'm reading my linear algebra textbook and there are two sentences that make me confused.

(1) Symmetric matrix $A$ can be factored into $A=Q\lambda Q^{T}$ where $Q$ is orthogonal matrix : Diagonalizable
($Q$ has eigenvectors of $A$ in its columns, and $\lambda$ is diagonal matrix which has eigenvalues of $A$)

(2) Any symmetric matrix has a complete set of orthonormal eigenvectors
whether its eigenvalues are distinct or not.

Diagonalizable means the matrix has n distinct eigenvectors (for $n$ by $n$ matrix).
If symmetric matrix can be factored into $A=Q\lambda Q^{T}$, it means that
symmetric matrix has n distinct eigenvalues.
Then why the phrase "whether its eigenvalues are distinct or not" is added in (2)?

After reading eigenvalue and eigenvector part of textbook, I conclude that every symmetric matrix is diagonalizable. Is that true?

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