Matrices

Basic Conceps
Theorem1. If matrices A, B, and C all have the same order,then
               (a) the commutative law of addition holds; that is,
 
                                   A + B = B + A
    
               (b) Tne associatiove law of addition holds; that is,

                             A + (B + C) = (A + B) + C

      Theorem2. If A and B are matrices of the same order and if a and b 
           denoted scalars, then the following distributive laws hold:
                (a) a(A + B) = aA + aB
                (b) (a + b)A = aA + bA
                (c) (ab)A = a(bA)

Matrix Multiolication
      Theorem   If A, B and C have appropriate orders so that the 
           following additions and multiplications are defined, then
                (a) A(BC) = (AB)C  (associate law of multiplication)
                (b) A(B + C) = AB + AC (left distributive law)
                (c) (B + C)A = BA + CA (right distributive law)


Determinants
Properties of Determinants
Eigenvectors and Eigenvalues
Properties of Eigenvextors and Eigenvalues