Know About Matrix

The Matrix can be demonstrated as a group of numbers that are arranged in the form of columns and rows. In the rows and columns of the Matrix, the numeric value written is called the elements. Along with this, the elements of the Matrix are also known as the entries of the Matrix. The definition of a Matrix is very easy. The simple definition is the arrangement of numbers in the rows and columns. Along with this, the arrangement of numerical values in the rectangular column is also called the Matrix. Matrix is an array or table sometimes. 

Definition of Matrix 

Let’s learn about the definition of the Matrix. 

The Matrix is described as an array of numbers arranged in rows and columns. The Matrix is used to describe mathematical concepts. However, in mathematics, both determinants and matrices are interrelated. 

The basic definition of Matrix or types of Matrix 

Let’s understand some basic definitions of the matrix. We also learn the definition of Matrix with examples. 

In mathematics, there are ten types of Matrix. These are:

• Row matrix 

• Column matrix 

• Square Matrix 

• Lower triangular Matrix 

• Zero Matrix 

• Upper triangular Matrix

• Diagonal Matrix 

• Scalar matrix

• Unit matrix 

• Comparable Matrix 

Row matrix 

The row matrix is a type of Matrix that only contains elements in the row. It does not contain any element in the column. In simple words, all the column elements in such a matrix remain null. Row matrix example:

A = [ 2  3  4] 

The above Matrix is the row matrix. 

Column matrix 

A column matrix is a type of Matrix which is just opposite the row matrix. In the column matrix, the elements are only present in the column. The elements in the row remain null. 

Square Matrix 

It is a type of Matrix in which the number of columns remains equal to the number of columns. In this Matrix, if the number of elements in the row is 3, then the number of elements in the column will also remain the 4. Square matrix example. 

A= [1] 

It is the 1×1 Matrix, where the number of rows and columns is equal to the one. 

Zero Matrix

The zero Matrix is a type of Matrix. In this Matrix, all the elements remain zero. Whether the zero Matrix contains 4 rows or 5 columns, the elements of the zero Matrix will remain zero. That’s why it is often called the null Matrix. 

Zero matrix example:

A= [0  0  0] 

In the above example, there are one row and three columns. All the elements of rows and columns are zero. 

Upper triangular Matrix

The upper triangular Matrix is that Matrix that only contains elements in the upper entries. In this type of Matrix, the numeric value is given to those elements only who lie either on the diagonal or above the diagonal. All the elements below the diagonal remain zero in the upper triangular Matrix. 

Lower triangular Matrix

The lower triangular Matrix is just the opposite of the lower triangular Matrix. The Matrix only contains elements in the upper entries. In this type of Matrix, the numeric value is given to those elements only who lie either on the diagonal or below the diagonal. All the elements above the diagonal remain zero in the lower triangular Matrix. 

Diagonal matrix 

The diagonal Matrix is the unique Matrix. The element which lies in the diagonal only contains the numeric value in this type of Matrix. All the elements above and below the diagonal contain zero value in the diagonal Matrix.

Scalar matrix

It is a type of Matrix in which all the values of the diagonals remain the same. If the value of one diagonal is zero, then the other diagonal will also have a zero value. 

Unit matrix 

The unit matrix is a type of Matrix that only contains elements in the diagonal, and the value if all its elements remain 1 only. 

Comparable matrix 

Comparable matrices are those matrices that have the same dimensions and the same order. 

Matrix formulas

The matrix formulas include various formulas. Some are described here, 

• Addition of two matrix = A+ B

• Subtraction of Matrix: B-A

• Multiplication: A. B

• Division: A/B

So, almost all the matrix formulas of Matrix will remain basic mathematical formulas.

Conclusion 

The Matrix is a very broad study. There are many matrix formulas used to solve the different mathematical problems. Unit matrix id is the unique Matrix. It Is also called an identity matrix. All the elements in the identity matrix remain zero, expecting the elements of diagonal. The identity or unit matrix is used to find the transposition in the Matrix. It is also used to solve the various formulas and principles, including Cramer’s rule. The definition of Matrix is not limited to the set of rows and columns, but it is very broad in terms of arrays and entries.