Difference between revisions of "Diagonal matrix"
From Encyclopedia of Mathematics
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| + | ''quasi-scalar matrix'' | ||
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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 $(n\times n)$ 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&\cdots&0\\0&a_2&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&\cdots&\cdots&a_n\end{pmatrix},$$ |
where the $a_i$ are elements of $K$. | where the $a_i$ are elements of $K$. | ||
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| + | See also: [[Defective matrix]]. | ||
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| + | ====References==== | ||
| + | * A.C. Aitken, "Determinants and matrices", Oliver and Boyd (1939) {{ZBL|65.1111.05}} {{ZBL|0022.10005}} | ||
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| + | [[Category:Special matrices]] | ||
Latest revision as of 03:37, 25 February 2022
2020 Mathematics Subject Classification: Primary: 15B [MSN][ZBL]
quasi-scalar matrix
A square matrix in which all entries — with the possible exception of the elements on the main diagonal — are zero.
Comments
I.e. an $(n\times n)$ diagonal matrix over a field $K$ has the form
$$\begin{pmatrix}a_1&0&\cdots&0\\0&a_2&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&\cdots&\cdots&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=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