Introduction to Matrices

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• Misc
  • Another colloquium coming up Thursday after break (Oct. 15) - more then
• Questions?
• Matrices
  • Sections 9.1 and 9.2
    • Matrix = 2D array - rows and columns
    • Commas separate columns, semicolons rows
    • Element access: myArray( row, column )
    • Linear indexing w/ 1 index counting down columns from first
    • Out-of-bounds access
      • Error if fetching element value
      • Adds element if assigning
  • Examples
    • Create matrix
      

      >> m1 = [ 1 2 3; 10 20 30 ]
      m1 =
           1     2     3
          10    20    30
      >> m1'
      ans =
          1    10
          2    20
          3    30

    • Access and change elements
      

      >> m1(6)
      ans =
          30
      >> m1(2,3)
      ans =
          30
      >> m1(3)
      ans =
          2
      >> m1(2) = 100
      m1 =
           1     2     3
         100    20    30

    • Other matrix creation functions
      

      >> zeros( 4 )
      ans =
           0     0     0     0
           0     0     0     0
           0     0     0     0
           0     0     0     0
      >> zeros( 2, 4 )
      ans =
           0     0     0     0
           0     0     0     0
      >> eye( 3 )
      ans =
           1     0     0
           0     1     0
           0     0     1
      >> rand( 3, 5 )
      ans =
          0.9706    0.8003    0.9157    0.6557    0.9340
          0.9572    0.1419    0.7922    0.0357    0.6787
          0.4854    0.4218    0.9595    0.8491    0.7577
      >> rand( 3 )
      ans =
          0.7431    0.1712    0.2769
          0.3922    0.7060    0.0462
          0.6555    0.0318    0.0971
      >> rand( 1, 10 )
      ans =
        Columns 1 through 6
          0.8235    0.6948    0.3171    0.9502    0.0344    0.4387
        Columns 7 through 10
          0.3816    0.7655    0.7952    0.1869

• Matrices Lab
  • Handout
  • Indexing sections of a matrix in stickPerson function
    • Vector of indices picks multiple rows or columns, much as with vectors
    • Single colon as row or column index indexes all rows or columns
      

      >> v = 1 : 7
      v =
           1     2     3     4     5     6     7
      >> v( 2: 4 )
      ans =
           2     3     4
      >> m1
      m1 =
           1     2     3
         100    20    30
      >> m1( 1, 1:2 )
      ans =
           1     2
      >> m1
      m1 =
           1     2     3
         100    20    30
      >> m1( 1, : )
      ans =
           1     2     3

  • Matrix multiplication
    • Row-by-column sum of products
    • Lots of geometric transformations of points can be expressed as matrix multiplication
      
      

      >> m1 = [ 2 4 6; 7 8 9 ]
      m1 =
           2     4     6
           7     8     9
      >> m2 = [ 10 20; 30 40; 3 5 ]
      m2 =
          10    20
          30    40
           3     5
      >> m1 * m2
      ans =
         158   230
         337   505
      >> m3 = eye(2)
      m3 =
           1     0
           0     1
      >> m2
      m2 =
          10    20
          30    40
           3     5
      >> m3 * m2
      {Error using *
      Inner matrix dimensions must agree.}

  • Examples of original and possible transformed stick person
    

    >> stickPerson

    
    
    

    >> drawFigure( tilt )  % drawFigure and tilt are parts of my solution

    
    
• Next
  • Matrix operations
  • Read sections 9.3 and 9.4

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