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MATRIX IS JUST ANOTHER NUMBER

   

    Matrix is square or rectangular table of numbers arranged in rows and columns.  It looks simple.  But its potential is immense.
     If matrix is just another kind of numbers like integers, fractions, what is 0,1,-1 and i in matrix-kind.  We will find out.

    First, we should learn matrix multiplication.
         Multiplication of matrices is the important operation and it is highly useful.  To multiply two matrices, number of rows of one matrix must be equal to the number columns of another matrix.

 MULTIPLYING MATRIX A AND B

 [a b  * [e f   = [ae +bg  af +bh
 c d]     g h]     ce +dg   cf +dh]
  A         B     =           C

 This is how you multiply order of two matrices.
     Column elements in one matrix is multiplied by corresponding row elements in another matrix and summed up to get the new element.
Why we multiply this way?
Consider this set of equations.
4x +2y+z  = 10
2x +3y+4z =25

 [4 2 1  * [x  = [10
 2 3 4]     y      25]
               z]
    If you multiply the matrices following the rules, you will get back the equations.  That is matrix.  Again, if we follow the rules of matrix multiplication, the matrix operators and matrix entities will hold good.

 '0' is the null matrix as
0 = [0 0
       0 0]  order of 2, must be square
0 =[000
      000
      000] order of 3
       this, we can understand

 unit matrix = '1' = I = [1 0     
                                     0  1]
 or [100
      010
      001]
I*1 must be 1.  1*0 =0; only this arrangement of matrix will meet these conditions.

    -1 = [-1 0
            0 -1]
     It is also logical.  -1*-1 must be +1.
If you multiply above matrix by itself, it will yield unit matrix.

 What about i, the imaginary number
 i = [o -1
       1  0]
If you find i^2, it will be equal to -1.  Hence the matrix for 'i' is correct.
    A matrix can have any order.  It can be rectangular.  It can be 3 or more dimensional.

 Operations of Matrix:
     If two matrices have equal dimensions, each corresponding element in them can be added.  Subtraction can be done in the same way.  There is no division operation for matrices.
     But 'inverse of matrix' can be found.  The procedure is complicated one.
    
     We can perform magic with matrix.  For example in Artificial intelligence, face recognition software uses matrices.   
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