Properties Of Matrices

Properties of Matrices-1:

Identity Matrix: A scalar matrix whose a_ij = 1 for all i = j. An identity matrix of size n n is commonly denoted by I_n.

Example:

Symmteric Matrix: A matrix A = [a_ij ]nn is symmetric to its main diagonal if a_ij = a_ji for i = 1,2,.....,n and j = 1,2.....,n.

Example:

Equality between Two Matrices:

Example:

Arithmetic Operation:

Example:

Proprties of Matrix Addition:

If the matrix A,B,C and the null matrix O are of the same size, then

1. A B = B A (Commutative Law)

2. A (B C) = ( A B ) C (Associative Law)

3. A O = O A = A

4. Each matrix A has negative, -A, such that A ( - A) = O.