Difference between revisions of "Diagonal matrix"
From Encyclopedia of Mathematics
(also quasi-scalar matrix, cite Aitken (1939)) |
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I.e. an 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=44574
Diagonal matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Diagonal_matrix&oldid=44574
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article