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Difference between revisions of "Diagonal matrix"

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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
  
$$\begin{pmatrix}a_1&0&\ldots&0\\0&a_2&\ldots&0\\\ldots&\ldots&\ldots&\ldots\\0&\ldots&\ldots&a_n\end{pmatrix},$$
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$$\begin{pmatrix}a_1&0&\cdots&0\\0&a_2&\cdots&0\\\vdots&\vdots&\ddots&\vdots\\0&\cdots&\cdots&a_n\end{pmatrix},$$
  
 
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====
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* 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

How to Cite This Entry:
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