Calculations with Matrices

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Previous Lecture

• Misc
  • Colloquium
    • “The Group Menagerie”
    • Dr. Elizabeth Wilcox, SUNY Oswego
    • Thursday (tomorrow), Oct 15, 4:00
    • Newton 202
    • Extra credit for short write-ups, as usual
  • First hour exam
    • Next Friday, Oct. 23
    • Material from start of semester through matrices (e.g., arithmetic, scripts & functions, vectors, plotting, matrices, etc.)
    • 3 - 5 short-answer questions
      • Precise Matlab syntax will only matter at the “what I expect” vs “perfect” level
    • Full class period
    • Open book, notes, computer; closed person
• Questions?
• Matrix Operations
  • Sections 9.3 and 9.4
    • Same operators as in 1D apply to 2D
    • Left and right division…
      • Backwards divide (\) solves systems of linear equations
        
        

        M = [ 2 -1; 1 1 ]
        M =
             2    -1
             1     1
        S = [5;6]
        S =
             5
             6
        M\S
        ans =
            3.6667
            2.3333

    • Element-wise operations
    • Multiplication
      • a * b requires a to have same number of columns as b has rows
      • Not commutative
    • rand function builds n row by m column matrix of random numbers between 0 and 1
      • randi(iMax) generates random integer from 1 to iMax
      • Can also give matrix dimensions
    • Reduce operations (e.g., sum, max, etc.) work along columns of matrices
  • Examples
    • Find the maximum element in a matrix
      

      m = rand( 3, 4 )
      m =
          0.8147    0.9134    0.2785    0.9649
          0.9058    0.6324    0.5469    0.1576
          0.1270    0.0975    0.9575    0.9706
      max( m )
      ans =
          0.9058    0.9134    0.9575    0.9706
      max( max(m) )
      ans =
          0.9706

    • What does matrix exponentiation (e.g., m^2) do?
      • Multiply a matrix by itself n times
        

        s = [ 2 3; 4 5 ]
        s =
             2     3
             4     5
        s ^ 2
        ans =
            16    21
            28    37

  • Matrices and 3D plotting project handout
• Matrix lab
• Next
  • Concatenating and slicing matrices
  • Read sections 9.5 through 9.8

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