Difference between revisions of "Diagonal matrix"
From Encyclopedia of Mathematics
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A square matrix in which all entries — with the possible exception of the elements on the main diagonal — are zero. | A square matrix in which all entries — with the possible exception of the elements on the main diagonal — are zero. | ||
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| − | I.e. an | + | I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form |
| − | + | $$\begin{pmatrix}a_1&0&\ldots&0\\0&a_2&\ldots&0\\\ldots&\ldots&\ldots&\ldots\\0&\ldots&\ldots&a_n\end{pmatrix},$$ | |
| − | where the | + | where the $a_i$ are elements of $K$. |
Revision as of 15:10, 23 April 2014
A square matrix in which all entries — with the possible exception of the elements on the main diagonal — are zero.
Comments
I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form
$$\begin{pmatrix}a_1&0&\ldots&0\\0&a_2&\ldots&0\\\ldots&\ldots&\ldots&\ldots\\0&\ldots&\ldots&a_n\end{pmatrix},$$
where the $a_i$ are elements of $K$.
How to Cite This Entry:
Diagonal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Diagonal_matrix&oldid=31902
Diagonal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Diagonal_matrix&oldid=31902
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article