Matrix is an important topic in mathematics that deals with operations to solve complex problems in an easy and fun to do manner. There are six different types of matrices in mathematics. In mathematics, linear algebra mainly consists of different matrices and uses them in different scenarios. This article aims to provide you with comprehensive knowledge of diagonal Matrix, triangular, square, identity, symmetric, and orthogonal matrices. Let’s get started with an introduction to different types of matrices with suitable examples to make you understand the concept of matrices better.

Introduction to different types of matrices

The different types of matrices are diagonal, triangular, square, identity, symmetric, and orthogonal matrices. Let’s dive deep into each type with their suitable examples. 

Diagonal Matrix

A diagonal Matrix can be defined as a matrix with zero values except the main diagonal. In a matrix, the main diagonal is considered from the top-left value of the Matrix to the bottom right value of the Matrix. This can be better understood with an example of a 3 x 3 matrix where the diagonal consists of elements .

D is used as a notation to denote a diagonal matrix. 

You may be wondering that in a square Matrix, we take the Matrix’s main diagonal as non-zero values. All the other values should be zero, but how to configure the main diagonal in a rectangular matrix. The shortest path or dimension is the main diagonal in a rectangular matrix. For example, if we take a matrix of 3 x 4, then the main diagonal will consist of elements (1,1),(2,2),(3,3),.

Square Matrix

You all know the denotations we used to denote rows and columns. If we denote rows by m and columns by n, the square Matrix is defined as a matrix with an equal number of rows and columns. If m=n or no. of rows equals no. of columns, then we can say that the particular Matrix is square. 

Triangular Matrix 

As the name suggests, the triangular Matrix can be defined as a matrix with either the lower left or upper right portion of the Matrix filled with non-zero values and the rest of the Matrix filled with zero value elements. In simple words, if we consider a matrix of 3×3, then it should have either (1,1),(1,2),(1,3),(2,2),(2,3),(3,3) filled with non-zero values. To become a triangular Matrix, all the other elements above or below the main diagonal should be zero .

Symmetric Matrix 

Symmetric Matrix refers to a matrix that consists of the same values in the Matrix’s top right and bottom right triangle. Let’s make it easier with an example of a 3×3 matrix. To be a symmetric matrix, all the top right and bottom right triangle values should be the same with the same signs. For example:

Identity Matrix 

An identity Matrix can be a subset of a square matrix with elements apart from the main diagonal as zero and all the elements in the main diagonal as one. These specific values function as identity metrics. It should not change any vector in the Matrix whenever it is multiplied. For example, suppose there is a square matrix of order three, i.e. a square matrix with three rows and three columns. In that case, all the values apart from (1,1),(2,2),(3,3) equals zero, and all these three values equal one.

Orthogonal Matrix 

An orthogonal matrix can be defined as a matrix whose dot product equals zero. There are several other definitions of Orthogonal Matrix apart from these, like a matrix is said to be orthogonal if its inverse can be calculated from its transpose. Orthogonal matrices are mostly used to calculate linear transformations like permutations and reflections.

Applications of Matrices

There are several uses of matrices ranging from basic mathematics to complex algorithms. Below are a few of the many applications of matrices.

Encryption- Used in the key generation for encryption and decryption

3D Games – Used in object altering 

Businesses and Economics – Used to study business trends and other things 

Construction – To construct complex architectures 

Physics – to deduce complex algosMatrices are fun, aren’t they? Here is a comprehensive guide on different types of mattresses, including diagonal Matrix, scalar Matrix, and identity matrix.

 Conclusion 

The concept of the Matrix was founded by Arthur Cayley, who is considered the father of the Matrix. Matrices have several physical and industrial uses to solve complex problems using simple Matrix calculations. There are six different types of matrices with their particular uses in different styles of problems. The matrix concept is full of operations of different types like addition, multiplication, inverse, and much more. This article has all the information about different types of matrices in easy-to-understand form and with suitable examples to help you easily understand the concept of matrices and their different types.