Math Doubts

Diagonal Matrix

A matrix that consists of zeros as entries (or elements) outside the main diagonal is called a diagonal matrix.

Introduction

diagonal matrix

Square matrices are appeared with zeros. In a special case, a square matrix contains zero as non-diagonal elements but it contains elements only on principal diagonal. Due to having elements on leading diagonal and having zeros as non-diagonal elements, the square matrix is recognized as a diagonal matrix.

M = e 1⁣1 0 0 0 0 e 2⁣2 0 0 0 0 e 3⁣3 0 0 0 0 e m⁣m

The matrix is having elements e1⁣1, e2⁣2, e3⁣3, em⁣m only on principal diagonal but observe the elements on non-diagonal areas. All are zero elements at non-diagonal areas. Therefore, this type of matrix is called a diagonal matrix. The diagonal elements can be either equal or unequal elements.

It is simply expressed as M = diag e 1⁣1, e 2⁣2, e 3⁣3, e n⁣n

Example

D is a square matrix of order 5×5. It is having 25 element in five rows and five columns.

D = 1 0 0 0 0 0 5 0 0 0 0 0 7 0 0 0 0 0 3 0 0 0 0 0 9

The matrix D is having two types of elements. One type of elements are nonzero elements and remaining all are zeros. Nonzero elements (1, 5, 7, 3 and 9) are placed on the leading diagonal and remaining non-diagonal elements are zeros. Therefore, the matrix D is known as a diagonal matrix.

The diagonal matrix D is written in simple form D = diag 1, 5, 7, 3, 9

Math Doubts

A best free mathematics education website for students, teachers and researchers.

Maths Topics

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Maths Problems

Learn how to solve the maths problems in different methods with understandable steps.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2021 Math Doubts, All Rights Reserved