The document discusses various types of matrices and their properties, including square, row, column, diagonal, scalar, identity, null, upper triangular, lower triangular, and triangular matrices. It highlights the importance of matrices in fields such as science, engineering, and economics for solving equations and analysis. Additionally, it includes definitions of equality for matrices and provides a video tutorial for further learning.

1. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Tutorial-I: Matrices
Basic Mathematics:
Matrices
Dr. Mehar Chand
Department of Mathematics
Baba Farid College, Bathinda-151001
April 21, 2020
Dr. Mehar Chand Properties Associated with Sphere

2. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Contents
1 Introduction
2 Types of Matrices
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular matrix
Lower triangular matrix
Triangular matrix
3 Equality of matrix
4 Full video Lecture
Dr. Mehar Chand Properties Associated with Sphere

3. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Introduction
The Matrices play very important role in Science, Engineer-
ing, Business and Economics. There are many applications
in various topics such as solving simultaneous equations,
linear programming, input-output analysis etc.
Definition (Matrix)
A matrix of order m × n (can be read as m by n) is an
ordered rectangular arrangement of m, n numbers or
functions consisting of m rows and n columns and is
defined as: A = [aij ]m×n
Dr. Mehar Chand Properties Associated with Sphere

4. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Square Matrix
Definition (Square Matrix)
A matrix A = [aij ]m×n is called a square matrix if m = n i.e.
the number of rows are equal to columns.
Dr. Mehar Chand Properties Associated with Sphere

5. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Row Matrix
Definition (Row Matrix)
A matrix A = [aij ]m×n is called a row matrix if m = 1 i.e. the
matrix has only one row.
Dr. Mehar Chand Properties Associated with Sphere

6. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Column Matrix
Definition (Column Matrix)
A matrix A = [aij ]m×n is called a column matrix if n = 1 i.e.
the matrix has only one column
Dr. Mehar Chand Properties Associated with Sphere

7. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Diagonal Matrix
Definition (Diagonal Matrix)
A square matrix A = [aij ]m×n is called a Diagonal Matrix if
aij = 0 for i = j and aij = 0 for i = j . a11, a22, ... are called
diagonal elements of square matrix. The diagonal elements
are said to constitute principal diagonal or simply
diagonal of the matrix.
Dr. Mehar Chand Properties Associated with Sphere

8. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Scalar Matrix
Definition (Scalar Matrix)
A matrix A = [aij ]m×n is called a Scalar matrix if aij = a for
i = j and aij = 0 for i = j.
Dr. Mehar Chand Properties Associated with Sphere

9. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Identity Matrix
Definition (Identity Matrix)
A matrix A = [aij ]m×n is called a Identity matrix if aij = 1 for
i = j and aij = 0 for i = j.
Dr. Mehar Chand Properties Associated with Sphere

10. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Null (or Zero) Matrix
Definition (Null (or Zero) Matrix)
A matrix A = [aij ]m×n is called a Null (or Zero) Matrix if each
elements of the matrix are zero. The zero matrix of order
m × n is usually denoted by Om×n or O
Dr. Mehar Chand Properties Associated with Sphere

11. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Upper triangular matrix
Definition (Upper triangular matrix)
A square matrix A = [aij ]n×n is called a Upper triangular
matrix if aij = 0 for i > j. In other words we can say that a
square matrix is an upper triangular matrix is all the
elements below the principal diagonal are zero.
Dr. Mehar Chand Properties Associated with Sphere

12. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Lower triangular matrix
Definition (Lower triangular matrix)
A square matrix A = [aij ]n×n is called a Upper triangular
matrix if aij = 0 for i < j. In other words we can say that a
square matrix is an Lower triangular matrix is all the
elements above the principal diagonal are zero.
Dr. Mehar Chand Properties Associated with Sphere

13. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Triangular matrix
Definition (Triangular matrix)
A square matrix A = [aij ]n×n is called a triangular matrix if it
is either upper triangular matrix or lower triangular matrix.
Dr. Mehar Chand Properties Associated with Sphere

14. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Equality of matrices
Definition (Equal of matrix)
Two matrices A = [aij ]m×n and B = [bij ]m×n are said to be
equal if they are of same order and their corresponding
elements are equal.
Dr. Mehar Chand Properties Associated with Sphere

15. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Full video Lecture
To see full video lecture visit the below link
https://youtu.be/hEId2ZuD4Qc
Dr. Mehar Chand Properties Associated with Sphere

16. Properties
Associated
with Sphere
Dr. Mehar
Chand
Introduction
Types
Square Matrix
Row Matrix
Column Matrix
Diagonal Matrix
Scalar Matrix
Identity Matrix
Null Matrix
Upper triangular
matrix
Lower triangular
matrix
Triangular matrix
Equality of
matrix
Video
Thank you
Dr. Mehar Chand Properties Associated with Sphere