Nice and Tidy at 10:19, 11 February 2008

2008-02-11T10:19:23Z

← Older revision		Revision as of 12:19, 11 February 2008
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	==References==		==References==
	*[http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrix entry in Wikipedia]		*[http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrix entry in Wikipedia]
			[[category: mathematics]]

Dduque: 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 $i$ th ro...

2008-02-11T10:00:03Z

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...

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 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:
:<math>a_{i,j} = a_{j,i}^*. </math>

If the conjugate transpose of a matrix <math>A</math> is denoted by <math>A^\dagger</math>, then this can concisely be written as

:<math> A = A^\dagger. \,</math>

For example,

:<math> \begin{bmatrix}3&2+i\\ 2-i&1\end{bmatrix} </math>

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]]).

==References==
*[http://en.wikipedia.org/wiki/Hermitian_matrix Hermitian matrix entry in Wikipedia]

Hermitian matrices - Revision history

Nice and Tidy at 10:19, 11 February 2008

Dduque: 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 ith ro...

Dduque: 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 $i$ th ro...