There are numerous matrices used in linear algebra. The different matrices can be different based on their element or order and a certain range of conditions. The term “Matrices” is the plural name for a matrix and is not the most commonly used to describe “matrices”. In this article, we’ll discover the most commonly utilised forms of matrices and their definitions with examples.
By understanding the different types of matrices, better efficiency in understanding their application can be gained.
What are Different Kinds of Matrices?
This article will discuss some of the major types used in engineering, mathematics and science. Here’s a perfect listing of the most frequently used kinds of matrices for linear algebra:
- Rectangular Matrix
- Square Matrix
- Identity Matrices
- Row Matrix
- Column Matrix
- Singleton Matrix
- Diagonal Matrix
- Matrix of Ones
- Zero Matrix
It is possible to use these various kinds of matrices to arrange data according to individual, age, company, month, and the list goes on. This allows us to use the data to make choices and solve many math-related problems.
Identifying Kinds of Matrices Based on Dimension
They come in multiple sizes; however, generally, their shapes are identical. The matrix’s size is defined as its dimension. It is the total amount of columns and rows in the given matrix.
1. Row and Column Matrix
Matrices that have one column and any of them are referred to as row matrices. Likewise, matrices with just one row and one column are known as column matrices.
2. Rectangular and Square Matrix
A matrix that doesn’t have an identical number of columns and rows is an irregular matrix. A rectangular matrix can be identified by [B]mxn. Any matrix with the same number of columns and rows is known as a square matrix. A square matrix is indicated by [B]nxn.
3. Constant Matrices
Constant matrices are those in which all elements are constants for a given size/dimension of the matrix. The matrix elements are identified by bij. Let’s examine these kinds of matrices whose elements remain constant.
4. Identity Matrix
The matrix of identity is one of the square diagonals, in which all elements on the diagonal equal 1 and the other parts are equal to zero. It is identified by the letter I.
5. Matrix of Ones
Any matrix where all components are equivalent to one is called a one-dimensional matrix.
6. Zero Matrix
Any matrix where all components are equivalent to zero is known as a zero matrix.
Other Kinds of Matrices
In addition to the most widely used matrices, there exist different types utilised in advanced math and computer technology. Below are some other types found in application:
1. Singular and Non-singular Matrix
Any square matrix that has a determinant greater than zero is referred to as a singularity matrix. A matrix with a determinant that is not equal to zero is known as a non-singular matrix. The determinant of a matrix can be determined using the formulas for determining.
2. Diagonal Matrix
A square matrix where all elements are zero apart from those diagonal is referred to as a diagonal matrix. Let’s look at the different types of diagonal matrices. A Scalar matrix is a particular kind of diagonal square in which all diagonal elements are equal.
3. Upper and Lower Triangular Matrix
A triangular upper is a square in which all the elements beneath the diagonal elements have zero. A lower triangular matrix is a quadrilateral matrix in which all the elements present above the diagonal elements are zero.
4. Symmetric and Skew Symmetric Matrix
A square matrix D with a size of nxn will be considered symmetric when and only if DT = D. An F-square matrix with a size of Nxn is thought to be skew-symmetric; it is only the case if FT= F.
5. Stochastic Matrices
A stochastic matrix can be described as a type of matrix where every entry represents the probability. It is thought of as stochastic when all entries are not negative, and the columns’ entries total 1. In the same way, a matrix that has all of its entries being non-negative so that the entries in every row add to 1 is known as a right stochastic one.
6. Orthogonal Matrix
The square-shaped matrix B can be thought of as an orthogonal matrix in the case that B is x BT = I. Here, I represent an identity matrix, in which BT can be described as the transpose matrix of B.
Important Notes on Kinds of Matrices
Here’s a list of some points to be considered when looking at the different kinds of matrices
- Constant matrices are matrices in which all elements are constants in any size/dimension of the matrix.
- Matrices having the same column but with any row are referred to as column matrices.
- Matrices that have only one or and the possibility of having columns is referred to as row matrices.
How Do You Identify Kinds of Matrices?
One method to determine the kind that a particular matrix has is verifying its dimensions. A matrix’s dimension is defined as the total amount of columns and rows within the given matrix. Take the example of matrix B = [1 2 5 8 0]. There are five columns and one row for this particular matrix, which means that its dimension is 1 5.
If a matrix consists of one column and one row and columns, it could be considered to be an array of rows. Therefore it is an example of a row matrix.
Which Matrix Is Never Invertible?
The square-shaped matrix can be considered to be invertible only when its determinant isn’t greater than zero. For instance, a two-by-two matrix is invertible when the determinant of the matrix is not 0.
If the determinator for this particular matrix is zero and the matrix isn’t invertible, and cannot be able to reverse. Therefore, any single matrix with a determinant at or above zero is not invertible.
So, now that you know all about the different kinds of matrices, a few solved questions can help you get deeper into this. Mostly, Matrix related questions are good for scoring quick marks. They may be included in your Q-paper in the form of one-word answer questions, FITB, or even short answers.
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