1. DR.B.C.ROY ENGINEERING COLLEGE
NAME: SHOVAN GHOSH
COLLEGE ROLL NO.- 2219011
BRANCH: CIVILL ENGINEERING
SUBJECT: MATHEMATIC-IB
SUBJECT CODE: BS-M 102
TOPIC: WRITE A REPORT ON SYMMETRIC AND SKEW- SYMMETRIC MATRICES WITH EXAMPLES.
2. INTRODUCTION
Matrix: Matrix in mathematics is defined as an array of numbers arranged in a
rectangular fashion and divided between rows and columns. It contains all the
numbers arranged in square brackets. The operation of matrices is a very important
topic in mathematics for the board exams as well as for the engineering entrance
exams.
What is a Symmetric Matrix?
■ A square matrix that is equal to its transpose is known as a symmetric matrix.
■ Only square matrices are symmetric because only equal matrices have equal
dimensions.
■ A matrix A with nn dimensions is said to be skew-symmetric if and only if aij = aji
for all i, j such that 1≤n, j≤n.
■ Suppose A is a matrix, then if the transpose of matrix A = AT is equal, it is a
symmetric matrix.
3.
4. If any diagonal matrix is equal to the transpose of the matrix, such matrices are automatically
symmetric.
Before We Move Further, Let Us Know About Some Important Terms!
A square matrix is a matrix where the number of columns is equal to the number of rows.
■ If m=n, the matrix is a square matrix
■ If m ≠ n , the matrix is a rectangular matrix
Here, m = The number of rows
n = The number of columns.
What is a Skew Symmetric Matrix
■ A square matrix is said to be skew-symmetric if the transpose of the matrix equals its negative.
■ A matrix A with nn dimensions is said to be skew-symmetric if and only if
aij = -aji for all i, j such that 1≤n, j≤n.
■ Suppose A is a matrix, then if the transpose of matrix A, AT =- A is equal then it is a skew-symmetric
matrix.
5. METHODOLOGY
First, let us know how to find the Transverse of a Matrix
■ Transpose of a Matrix (AT)
We find the transpose of a matrix by interchanging the rows and columns of the
original matrix. Suppose the original matrix is denoted by n×m, the transpose of
the matrix will be m×n.
7. How to check Whether a Matrix is Symmetric or Not?
Step 1- Find the transpose of the matrix.
Step 2-Check if the transpose of the matrix is equal to the original matrix.
Step 3- If the transpose matrix and the original matrix are equal, then the
matrix is symmetric.
