A square matrix is a matrix with the same number of rows and columns. It can be classified as singular or nonsingular. Special types of square matrices include symmetric matrices where the matrix is equal to its transpose and skew-symmetric matrices where the matrix is equal to the negative of its transpose. Any square matrix can be uniquely expressed as the sum of a symmetric matrix and a skew-symmetric matrix using the formula C = (1/2)(C + C^T) + (1/2)(C - C^T).

1. SQUARE MATRIX

2. HELLO!
I am Sanjana Jahan
163-15-8443

3. WHAT IS SQUARE MATRIX?

4. In mathematics, a square matrix is
a matrix with the same number of
rows and columns. An n-by-n matrix
is known as a square matrix of
order n. Any two square matrices of
the same order can be added and
multiplied.

5. CLASSIFICATION OF SQUARE
MATRIX
Square
matrix
Singular
matrix
Nonsingular
matrix

7. SPECIAL SQUARE MATRIX
Special
Square
matrix
Symmetric
matrix
Skew-
symmetric
matrix

8. SYMMETRIC MATRIX

9. SKEW SYMMETRIC
MATRIX

10. TRUE FACTS :
 M+ MT is symmetric matrix
M-MT is skew-symmetric matrix.
M CAN be uniquely expressed as the sum of a
symmetric matrix and a skew-symmetric matrix.

11. DECOMPOSITION OF A SQUARE MATRIX INTO
SYMMETRIC AND SKEW SYMMETRIC MATRICES
Let Cn×n be a square matrix. We can write C = (1/2)(C + C t ) +
(1/2)(C − C t ) = A + B, where At = A is symmetric and Bt = −B
is skew-symmetric.

12. THANKS!
Any questions?