Types of Elements of Matrix
The components of the matrix are what are known as the matrix’s elements and they could be variables, numbers, a mix of the two, or any other kind of special character. Based on the position of these elements in the matrix, we can categorise these elements as:
- Diagonal Elements
- Off-Diagonal Elements
Let’s discuss these types in detail.
Diagonal Elements
A diagonal matrix is a square matrix in which all members are zero except for the primary diagonal elements. When dij = 0 and i is not equal to j, a square matrix D = [dij]n x n is referred to as a diagonal matrix.
For example if A =
[Tex]\begin{bmatrix} a \ 0 & \\ 0\ b & \end{bmatrix} [/Tex]
In the above 2×2 matrix, matrix A is a diagonal matrix. Here ‘a’ and ‘b’ are the diagonal elements.
Off Diagonal Elements
The fact that the matrix’s row number and column number are not equal represents the off-diagonal members. The first element of the first row and the last element of the last row combine to generate a major diagonal. The other elements in the matrix are referred to as non-diagonal or off-diagonal elements whereas the elements that are on the leading diagonal are referred to as diagonal elements.
For Example: If A =
[Tex]\begin{bmatrix} a \ 1 & \\ 0\ b & \end{bmatrix} [/Tex]
In the above 2×2 matrix, matrix A is a diagonal matrix. Here ‘1’ and ‘0’ are the off diagonal elements.
For Example: If B =
[Tex]\begin{bmatrix} a \ 1\ 0 & \\ c\ d\ 3 &\\ 0\ -1\ b & \end{bmatrix} [/Tex]
In the above 3×3 matrix, matrix B is a diagonal matrix with 1, 0, c, 3, 0 and -1 as off-diagonal elements.
Check: Types of Matrices
Elements of Matrix
Elements of the Matrix are the components or entries of the Matrix. These elements could be any variables, numbers, a mix of variables and numbers, or any other kind of special characters as well. The number of elements of a matrix is equal to the product of the number of rows and columns present in a matrix.
This article explores the concept of the element of matrix in detail and makes it easy to grasp for all the readers of the article without any regard to their academic level. All subtopics such as their meaning, definition, symbol, example, and many many more, are covered in the article with plenty of examples. So, let’s start our journey to the land of elements of the matrix and understand this concept.
Table of Content
- What is Matrix?
- What are Elements of a Matrix?
- Examples of Element of Matrix
- Types of Elements of Matrix
- Diagonal Elements
- Off Diagonal Elements
- Number of Elements of a Matrix
- Positions of Elements of Matrix
- Elements in Equal Matrices
- Properties of Matrix Elements
- Solved Problem on Elements of Matrix
- Practice Problems on Elements of Matrix