Math Doubts

Non-diagonal elements of a Square Matrix

The elements which do not lie on the leading diagonal of a square matrix is called non-diagonal elements of the matrix.

non diagonal elements
Non-diagonal elements in a matrix

The number of rows is equal to the number of columns in a square matrix. So, a principal diagonal is formed by the first element of first row and last element of last row. The elements which lie on the leading diagonal are known as diagonal elements but the remaining elements in the matrix are known as non-diagonal elements.

M = e 1⁣1 e 1⁣2 e 1⁣3 e 1⁣n e 2⁣1 e 2⁣2 e 2⁣3 e 2⁣n e 3⁣1 e 3⁣2 e 3⁣3 e 3⁣n e n⁣1 e n⁣2 e n⁣3 e n⁣n

e1⁣1 is the first element of first row and en⁣n is the last element of last row. They form a leading diagonal on which the elements e2⁣2, e3⁣3, e4⁣4 and etc. also lie.

Except these elements, all remaining elements are non-diagonal elements of the matrix.

Example

A is a square matrix of order 4×4. It is having 16 elements in four rows and four columns.

A = 4 1 3 0 3 2 7 9 5 8 4 6 6 2 1 7

The elements of matrix A is categorized into two types. One type of elements of this matrix is diagonal elements and other type of elements are non-diagonal elements.

The elements 4, 2, 4 and 7 lie on the leading diagonal but the remaining elements do not lie on the principal diagonal. In other words, 1, 3, 0, 7, 9 and 6 do not lie on the leading diagonal. Similarly, the elements 3, 5, 8, 6, 2 and 1 also do not lie on the principal diagonal.

Therefore, Except 4, 2, 4 and 7, the elements 1, 3, 0, 7, 9, 6, 3, 5, 8, 6, 2 and 1 are non-diagonal elements of the matrix A.

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