Math Doubts

Diagonal Matrix

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


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


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 Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved