Last updated on Saturday, September 30th, 2023

Types of matrices information is must for the different matrix operations. As you know, matrix has defined arrangements of the numbers within two close brackets. These numbers are called elements of the matrix.

Types of Matrices

A matrix is characterized by its rows and columns. Horizontal elements in the lines are known from the rows and verticals from the columns.

In general when we solve the matrices, we keep focus only on the operations e.g., mathematical multiplication, addition, subtraction, and division.

We are not bothered about the elements, from where these are taken. What is the original problem and purpose for which we are using the matrix formulation i.e., a mathematical approach?

For the beginners it is also equally important, so they understand the reason to apply it. If you are interested to know more about this please let us know. We will provide the detail information in the upcoming posts.

Okay, Now we will see the types of matrices for different matrix operation purposes.

#1. Scalar Matrix

The scalar matrix is square matrix and its diagonal elements are equal to the same scalar quantity. While off diagonal elements are zero.

For an example: Matrices A, B and C are shown below.  All the diagonal elements are same in magnitude, while off diagonal elements are zero.

It means a_ij =constant value; if i is equal to j order. This value will be equal to zero if i is not equal to j order.

#2. Triangular Matrix

The matrix who elements either below or above the the non- zero diagonal elements are zero. To understand this line first you see the matrix A in the below given picture.

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A & B are the two triangular matrices, because all the zero elements are above the diagonal elements. Also the diagonal elements are non zero. This type of matrices (Part-a) are called lower triangular matrices.

The matrices C & D are called uppler triangular matrices (part-b). The triangular matrix is square matrix.

#3. Null or Zero Matrix

All the elements of the null matrices are zero. This may be square, row or column matrix.

#4. Unit or Identity Matrix

A square matrix whose all diagonal elements are one (1) and rest of the elements are zero, called the unit matrix or identity matrix.

A, B & C matrices are an example of the Identity matrix.

A question for you. What do you think about the one row matrix which has all elements are equal to 1, does it would be identity matrix? Similar for the column matrix, which has all elements equal to 1.

I have started the types of matrices in reverse order, do you know the reason of it is what?  Actually, I thought you may be aware about the row and column matrices. But, if you are not aware about the row and column matrices, I will discuss that in below section.

#5. Diagonal Matrix

A diagonal matrix is always a square matrix , whose off diagonal elements are  always equal to zero. While diagonal elements are remain non zero.

Can you please tell me about the diagonal elements nature? Does from these numbers any one can be negative or zero?

In the above section we have seen the scalar matrix, can you please let me know the differences between diagonal and scalar matrices?

#6. Square Matrix

A square matrix has same number of rows and columns, as you can see in below given examples. The square matrix can have any type of integer like positive, negative and zero.

#7. Rectangular Matrix

In the rectangular matrix number of rows and columns are different. If rows are four columns may be 3 or 5 or any number different from the number 4.

The matrix have all types of integer as in to the square matrix you have seen. But you can not define the diagonal matrix elements.

#8. Column and Row Matrices

In the below given example you can see column and Rows matrices examples.  In the column matrix, you can observe that there is only one column while rows may be many.

On the other hand, in row matrix, row is one but columns may be many.

Conclusion

In this post you have observed some basic idea about the types of matrices.

The first point about it is the matrix have rows and columns.

Number of these rows and columns define the size and order of the matrix i.e., called dimension of the matrix.

The types of matrices you have checked here are scalar matrix, unit and identity matrix, null or zero matrix, triangular matrix, with both options lower and upper triangular matrices. Then diagonal matrix, rectangular matrix, row and column matrices.