http://www.sklogwiki.org/SklogWiki/index.php?title=Hermitian_matrices&feed=atom&action=historyHermitian matrices - Revision history2024-03-29T05:51:02ZRevision history for this page on the wikiMediaWiki 1.41.0http://www.sklogwiki.org/SklogWiki/index.php?title=Hermitian_matrices&diff=5656&oldid=prevNice and Tidy at 10:19, 11 February 20082008-02-11T10:19:23Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrix entry in Wikipedia]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>*[http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrix entry in Wikipedia]</div></td></tr>
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</table>Nice and Tidyhttp://www.sklogwiki.org/SklogWiki/index.php?title=Hermitian_matrices&diff=5644&oldid=prevDduque: New page: A '''Hermitian matrix''' (or self-adjoint matrix) is a square matrix with complex elements which is equal to its own conjugate transpose — that is, the element in the <math>i</math>th ro...2008-02-11T10:00:03Z<p>New page: A '''Hermitian matrix''' (or self-adjoint matrix) is a square matrix with complex elements which is equal to its own conjugate transpose — that is, the element in the <math>i</math>th ro...</p>
<p><b>New page</b></p><div>A '''Hermitian matrix''' (or self-adjoint matrix) is a square matrix with complex elements which is equal to its own conjugate transpose — that is, the element in the <math>i</math>th row and <math>j</math>th column is equal to the complex conjugate of the element in the <math>j</math>th row and <math>i</math>th column, for all indices i and j:<br />
:<math>a_{i,j} = a_{j,i}^*. </math><br />
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If the conjugate transpose of a matrix <math>A</math> is denoted by <math>A^\dagger</math>, then this can concisely be written as<br />
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:<math> A = A^\dagger. \,</math> <br />
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For example,<br />
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:<math> \begin{bmatrix}3&2+i\\ 2-i&1\end{bmatrix} </math><br />
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All eigenvalues of a Hermitian matrix are real, and, moreover, eigenvectors with distinct eigenvalues are orthogonal. The typical example of a Hermitian matrix in physics is the [[Hamiltonian]] (specially in [[quantum mechanics]]).<br />
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==References==<br />
*[http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrix entry in Wikipedia]</div>Dduque