What type of matrix

Matrices is plural for matrix. The following diagrams give some of examples of the types of matrices. Scroll down the page for more examples and explanations. A matrix may be classified by types. It is possible for a matrix to belong to more than one type. A row matrix is a matrix with only one row. A column matrix is a matrix with only one column. A zero matrix or a null matrix is a matrix that has all its elements zero. Matrices with only one row and any number of columns are known as row matrices and matrices with one column and any number of rows are called column matrices.

Let's look at two examples below:. Let's look at the examples below:. Let's look at these types of matrices whose elements are always constant. Apart from the most commonly used matrices, there are other types of matrices that are used in advanced mathematics and computer technologies. Following are some of the other types of matrices:. Any square matrix whose determinant is equal to 0 is called a singular matrix and any matrix whose determinant is not equal to 0 is called a non-singular matrix.

Determinant of a matrix can be found by using determinant formula. A square matrix in which all the elements are 0 except for those elements that are in the diagonal is called a diagonal matrix. Let's take a look at the examples of different kinds of diagonal matrices: A scalar matrix is a special type of square diagonal matrix, where all the diagonal elements are equal.

An upper triangular matrix is a square matrix where all the elements that are present below the diagonal elements are 0. A lower triangular matrix is a square matrix where all the elements that are present above the diagonal elements are 0.

Here, we can see that all the elements that are present below the main diagonal are 0. Hence, B is an upper triangular matrix. Let's consider the examples of two matrices D and F:. A matrix is considered to be a boolean matrix when all its elements are either 1s and 0s.

Let's consider the example of the matrix B to understand this better:. A stochastic matrix is a type of matrix whose all entries represent probability. A square matrix C is considered to be left stochastic when all of its entries are non-negative and when the entries in each column sum to 1. Similarly, a matrix with all its entries as non-negative such that entries in each row sum to 1 is called a right stochastic matrix. Consider the example of the matrix C here:. Take an example of the matrix B:.

Example 1: Which of the following is not a type of matrix? Solution: d Minor matrix cannot be considered as a type of matrix. Square, diagonal, and row matrices are various types of matrices. A diagonal matrix. A scalar matrix. A lower triangular matrix. An upper triangular matrix. Zero matrix. In a Symmetric matrix matching entries either side of the main diagonal are equal , like this:.