Types of Matrices- Definition, Classification

In linear algebra, there are many different types of matrices. All matrices are classified according to their elements, order, and a set of conditions. The plural version of a matrix is “matrices,” which is less usually used to refer to matrices.

Matrices come in a variety of sizes, but their shapes are usually the same. The total number of rows and columns that are present in a given matrix is considered as the matrix’s dimension.

• A matrix is a rectangular sequence of numbers or symbols arranged in rows and columns.

• Matrices is the plural form of matrix.

• A matrix’s size is known as a ‘n by m′ matrix and is expressed as m×n times , where m is the number of rows and n is the number of columns.

We have a 2×3 matrix here, for example, because the number of rows equals 3 and the number of columns equals 2.

    [2  5  6

     5  2  7]

Types of matrices:

Row matrix:

A row matrix can be defined as the matrix which has only one row. In a row matrix, the number of columns is irrelevant; all that counts is that there is only one row. A single row makes up a row matrix.

Example: [ 2  3  -1 ]

Column matrix:

A column matrix is similar to a row matrix, but with a few differences. The column matrix must have only one column to satisfy the criterion. It makes no difference how many rows there are in a column matrix; all that counts is that it has only one column.

Example: [ 6

                  6

                  7 ]

Rectangular matrix:

A rectangle matrix has a different number of rows and columns than a square matrix, and its size is m × n. Almost all matrices are rectangular in nature, but if the rows and columns are the same, the matrix is no longer rectangular.

Example: [ 1  2  5

                  4  3  8 ]

Square matrix:

When the rows and columns are equal, the matrix becomes a square matrix rather than a rectangle matrix. The explanation for this is simple: a square has all equal sides, and when the number of rows and columns are equal, all sides of a matrix are equal, hence the name square matrix.The primary diagonal is made up of parts of the form aij. The elements with i + j = n + 1 create the secondary diagonal.

Example: [ 2  4

                 -1  -5 ]

Upper triangular matrix:

Make a diagonal of the given matrix to comprehend the upper triangular matrix. You have an upper triangular matrix if all the entries below the diagonal are zero.

Example: [ 1  7  -2

                  0  -3  4

                  0   0  2 ]

Lower triangular matrix:

The difference between a lower triangular matrix and an upper triangular matrix is the position of the zeros. All of the elements above the diagonal in the lower triangular matrix are zero. We’ll call it a lower triangular matrix regardless of what’s below the diagonal, as long as the components above the diagonal are zero; nevertheless, the diagonal elements will never be 0 in either the upper or lower triangular matrix.

Example: [ 2  0  0

                  1  2  0

                  3  5  6 ] 

Diagonal matrix:

All the elements above and below the diagonal in a diagonal matrix are zeros. It’s similar to combining an upper triangular matrix with a lower triangular matrix.

Example: [ 2  0  0

                  0  3  0

                  0  0  5 ]

Scalar matrix: 

A scalar matrix is similar to a diagonal matrix, but with one exception. The scalar matrix must satisfy two requirements. The first is that all elements should be zero, both above and below the diagonal. The second requirement is that the diagonal elements must be identical. As a result, a scalar matrix is a diagonal matrix with equal diagonal members.

Example: [ 2  0  0

                  0  2  0

                  0  0  2 ]

Identity matrix:

A diagonal matrix with all diagonal members is called an identity matrix.

Example: [ 1  0  0

                  0  1  0

                  0  0  1 ]

Zero matrix:

All of the elements of a zero matrix are considered to be zero.

Example: [ 0  0

                  0  0 ]

Conclusion:

Matrices are classified according to their sequence, constituents, and other characteristics. Matrixes come in several forms.  All matrices are classified according to their elements, order, and a set of conditions.

Matrices come in a variety of sizes, but their shapes are usually the same. The total number of rows and columns in a given matrix is referred to as the matrix’s dimension.

In a row matrix, the number of columns is irrelevant; all that counts is that there is only one row.

A rectangular matrix has a different number of rows and columns than a square matrix, and its size is m × n.

When the rows and columns are equal, the matrix becomes a square matrix rather than a rectangle matrix. The explanation for this is simple: a square has all equal sides, and when the number of rows and columns are equal, all sides of a matrix are equal, hence the name square matrix.

All the elements above and below the diagonal in a diagonal matrix are zeros. It’s similar to combining an upper triangular matrix with a lower triangular matrix.

A diagonal matrix with all diagonal members are one is called an identity matrix.