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A start.
A '''Hermitian matrix''' is one that satisfies <math>M=M^\dagger</math>, where <math>M^\dagger</math> is the Hermitian conjugate of <math>M</math> (i.e., the matrix formed by transposing <math>M</math> and taking the complex conjugate of each element). As an example, the most general 2x2 Hermitian [[matrix]] has the form
<math>
\begin{pmatrix}
a & b \\
b^* & c
\end{pmatrix}
</math>
for arbitrary complex numbers <math>a,b,c</math>. In the case where all elements of the matrix are real, a Hermitian matrix becomes symmetric (as Hermitian conjugation then becomes equivalent to transposition).
==Properties of Hermitian matrices==
* The [[eigenvalue|eigenvalues]] are all real.
* The [[eigenvector|eigenvectors]] corresponding to different eigenvalues are orthogonal.
Because of these properties, Hermitian matrices have important applications in [[quantum mechanics]].
<math>
\begin{pmatrix}
a & b \\
b^* & c
\end{pmatrix}
</math>
for arbitrary complex numbers <math>a,b,c</math>. In the case where all elements of the matrix are real, a Hermitian matrix becomes symmetric (as Hermitian conjugation then becomes equivalent to transposition).
==Properties of Hermitian matrices==
* The [[eigenvalue|eigenvalues]] are all real.
* The [[eigenvector|eigenvectors]] corresponding to different eigenvalues are orthogonal.
Because of these properties, Hermitian matrices have important applications in [[quantum mechanics]].