Matrices
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Matrix definition:
+ same structure and look as an array
+ usually means rectangular or square, but could have more dimensions
+ a matrix is an array that represents a linear transformation

Notation for linear transformation:

    Ax = b
  
    A: coefficient matrix
    x: solution vector
    b: source vector

Example:

    2x-2y = 10 \     [ 2 -2] {x} = {10}
                >->  [-2  5] {y}   {20}
   -2x+5y = 20 /        A     x     b

 
What does all this mean?
+ So, matrix A transforms x into b
+ To find x, you need to solve the set of simultaneous equations
+ see "Solving Systems of Equations" in Mathematics Resources online
+ in MATLAB, try this:
  >> A=[2 -2;-2 5]; b=[10 20]'; x=A\b
     (see also $solve$)

Arithmetic Operations (copied from MATLAB HELP):

  +   Plus.
      X + Y adds matrices X and Y.  X and Y must have the same
      dimensions unless one is a scalar (a 1-by-1 matrix).
      A scalar can be added to anything.  
 
  -   Minus.
      X - Y subtracts matrix X from Y.  X and Y must have the same
      dimensions unless one is a scalar.  A scalar can be subtracted
      from anything.  
 
  *   Matrix multiplication.
      X*Y is the matrix product of X and Y.  Any scalar (a 1-by-1 matrix)
      may multiply anything.  Otherwise, the number of columns of X must
      equal the number of rows of Y.
 
  ^   Matrix power.
      Z = X^y is X to the y power if y is a scalar and X is square. If y is an
      integer greater than one, the power is computed by repeated
      multiplication. For other values of y the calculation
      involves eigenvalues and eigenvectors.
      Z = x^Y is x to the Y power, if Y is a square matrix and x is a scalar,
      computed using eigenvalues and eigenvectors.
      Z = X^Y, where both X and Y are matrices, is an error.
 
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