# Diagonal matrix

From Encyclopedia of Mathematics

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=52115

This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article