Types of Matrix
| Row Matrics | ( 1 2 3) |
| Column Matrics | 1 2 3 |
| Square Matrics (m=n) | 1 2 3 4 |
| Diagonal Matrics | 1 0 0 2 1 0 0 0 2 0 0 0 3 |
| Identity Matrics or Unit Matrics | 4 0 0
0 4 0 0 0 4 |
| Transpose of the Matrics | A= 1 2 3 4 AT = 1 3 2 4 |
Symmetric Matrics
A Square Matrics "A" is said to be a symmetric Matrics is the Transpose of the Matrics is equal to the "A-Matrix".
At = A
Example:
1 4 6
A = 4 2 -5
6 -5 3
1 4 6
At = 4 2 -5
6 -5 3
At = A
Skew Symmetric Matrix
A Square matrix "A" is said to be a Skew symmetric of the transpose as the matrix is equal to -A.
Example:
At = -A
0 -4 6
A = 4 0 -5
-6 5 0
0 4 6
At = -4 0 -5
-6 5 0
At = -A
0 -4 6
A = 4 0 -5
-6 5 0
0 4 6
At = -4 0 -5
-6 5 0
At = -A
Hermitian Matrix
A Square Matrix "A" is said to be Hermitian, if the conjugate transpose of the matrix is equal to the matrix itself
Example:
_
At = A
1 4+i 6i
A= 4i 2 -5
-6i -5 3
_ 1 4i 6i
A= 4+i 2 -5
-6i -5 3
_ 1 4+i 6i
At = 4i 2 -5
-6i -5 3
_
At = A
Skew Hermitian Matrix
A square matrix "A" is said to be skew Hermitian of the conjugate of transpose of the matrix is equal to
_
At = -A
Example:
0 4+i -1+6i
A= 4+i 2 -5
1+6i -5 0
_ 0 -4-i -1-6i
A= 4-i 0 -5
1+6i -5 0
_ 0 -4-i 1-6i
At = -4-i 0 5
-1-6i -5 0
_
At = -A
Orthogonal Matrix:
A Square matrix "A" is said to be orthogonal matrix
AAt =I
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