More Ways to Build Matrices

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• Misc
  • Colloquium
    • “The Eigenvalue Machine”
    • Dr. Kristopher Lee, Iowa State
    • Tuesday, March 1, 4:00 PM, Newton 214
    • Extra credit for write-ups
  • Exam 1
    • Next Wednesday (Mar. 2)
    • Material since beginning of semester (e.g., expressions, variables, vectors, plotting, matrices, functions, scripts, etc.)
    • 3 - 5 short-answer questions, may include writing short pieces of Matlab
    • Practice exam at http://www.geneseo.edu/~baldwin/math230/spring2016/exam1sample.pdf
    • Whole class period (50 minutes)
    • Open references (book, notes, computer); closed person
• Questions?
• Concatenating Matrices
  • Section 9.4
    • Concatenation joins arrays into larger ones
    • horzcat, vertcat and errors when numbers of rows/columns don’t agree
      
  • Example
    

    >> M = [ [1 2 3]; [4 5 6]; [7 8 9] ]
    M =
         1     2     3
         4     5     6
         7     8     9
    >> N = [ [ 10 11 12 ]; [13 14 15]; [16 17 18] ]
    N =
        10    11    12
        13    14    15
        16    17    18
    >> [ M , N ]
    ans =
         1     2     3    10    11    12
         4     5     6    13    14    15
         7     8     9    16    17    18
    >> horzcat( M, N )
    ans =
         1     2     3    10    11    12
         4     5     6    13    14    15
         7     8     9    16    17    18

• meshgrid
  • Section 11.8
    • Put all combinations of x, y values into 2D matrices
    • Incredibly useful for building tables
  • Example: compute table of x - y for x ranging from 1 to 5 and y from -2 to 2
    

    >> % subtraction table, x - y, x between 1 and 5, y between -1 and 3
    >> x = 1:5
    x =
         1     2     3     4     5
    >> y = -1:3
    y =
        -1     0     1     2     3
    >> meshgrid( x, y )
    ans =
         1     2     3     4     5
         1     2     3     4     5
         1     2     3     4     5
         1     2     3     4     5
         1     2     3     4     5
    >> [ Xtable, Ytable ] = meshgrid( x, y )
    Xtable =
         1     2     3     4     5
         1     2     3     4     5
         1     2     3     4     5
         1     2     3     4     5
         1     2     3     4     5
    Ytable =
        -1    -1    -1    -1    -1
         0     0     0     0     0
         1     1     1     1     1
         2     2     2     2     2
         3     3     3     3     3
    >> Xtable - Ytable
    ans =
         2     3     4     5     6
         1     2     3     4     5
         0     1     2     3     4
        -1     0     1     2     3
        -2    -1     0     1     2
    >> % Change which of x and y are vertical vs horizontal?
    >> [ Xtable, Ytable ] = meshgrid( y, x )
    Xtable =
        -1     0     1     2     3
        -1     0     1     2     3
        -1     0     1     2     3
        -1     0     1     2     3
        -1     0     1     2     3
    Ytable =
         1     1     1     1     1
         2     2     2     2     2
         3     3     3     3     3
         4     4     4     4     4
         5     5     5     5     5
    >> [ Ytable, Xtable ] = meshgrid( y, x )
    Ytable =
        -1     0     1     2     3
        -1     0     1     2     3
        -1     0     1     2     3
        -1     0     1     2     3
        -1     0     1     2     3
    Xtable =
         1     1     1     1     1
         2     2     2     2     2
         3     3     3     3     3
         4     4     4     4     4
         5     5     5     5     5

• 3D plotting project
  • Handout
• Matrix Lab
• Next
  • Summary / statistical operations on vectors and matrices
  • Read sections 7.9 and 9.5

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