Difference between revisions of "Diagonal matrix"
From Encyclopedia of Mathematics
(also quasi-scalar matrix, cite Aitken (1939)) |
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I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form | I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form | ||
| − | $$\begin{pmatrix}a_1&0&\ | + | $$\begin{pmatrix}a_1&0&\dots&0\\0&a_2&\dots&0\\\dots&\dots&\dots&\dots\\0&\dots&\dots&a_n\end{pmatrix},$$ |
where the $a_i$ are elements of $K$. | where the $a_i$ are elements of $K$. | ||
Revision as of 12:01, 14 February 2020
2020 Mathematics Subject Classification: Primary: 15B [MSN][ZBL]
quasi-scalar matrix
A square matrix in which all entries — with the possible exception of the elements on the main diagonal — are zero.
Comments
I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form
$$\begin{pmatrix}a_1&0&\dots&0\\0&a_2&\dots&0\\\dots&\dots&\dots&\dots\\0&\dots&\dots&a_n\end{pmatrix},$$
where the $a_i$ are elements of $K$.
See also: Defective matrix.
References
- A.C. Aitken, "Determinants and matrices", Oliver and Boyd (1939) Zbl 65.1111.05 Zbl 0022.10005
How to Cite This Entry:
Diagonal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Diagonal_matrix&oldid=43065
Diagonal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Diagonal_matrix&oldid=43065
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article