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					           Announcements
• Problem Set 2, handed out today, due next
  Tuesday.
• Late Homework should be turned into my
  office with date and time written on it.
• Mail problem sets in one zipped file to farrell
  (at) cs.umd.edu. When emailing matlab code
  to Ryan, use subject: CMSC 426 Matlab
  code.
     Matlab tutorial and Linear
         Algebra Review
•   Today’s goals:
•   Learn enough matlab to get started.
•   Review some basics of Linear Algebra
•   Essential for geometry of points and lines.
•   But also, all math is linear algebra.
•   (ok slight exaggeration).
•   Many slides today adapted from Octavia
    Camps, Penn State.
          Starting Matlab
• For PCs, Matlab should be a program.
• For Sun’s:
    Numerical


            Analysis and Visualization



                             Matlab 6.1
                  Help
• help
• help command
Eg., help plus
• Help on toolbar
• demo
• Tutorial:
  http://amath.colorado.edu/scico/tutorials
  /matlab/
       Matlab interpreter
• Many common functions: see help ops
                  Vectors
• Ordered set of
  numbers: (1,2,3,4)
• Example: (x,y,z)
  coordinates of pt in
  space.
Indexing into vectors
Vector Addition



     V+w
 v
     w
Scalar Product




       av
   v
     Operations on vectors
• sum
• max, min, mean, sort, …
• Pointwise: .^
            Inner (dot) Product
v   
        w


        The inner product is a SCALAR!
How do we prove these properties of the inner product? Let’s start with the fact that
orthogonal vectors have 0 inner product. Suppose one vector is (x,y), and WLOG
x,y>0. Then, if we rotate that by 90 degrees counterclockwise, we’ll get (y, -x).
Rotating the vector is just like rotating the coordinate system in the opposite direction.
And (x,y)*(y,-x) = xy – yx = 0.
Next, note that v*w = (v*w)/(||v||||w||) * ||v||||w|| This means that if we can show that
when v and w are unit vectors v*w = cos alpha, then it will follow that in general v*w =
||v|| ||w|| cos alpha. So suppose v and w are unit vectors.
Next, note that if w1 + w2 = w, then v*w = v*(w1+w2) = v*w1 + v*w2. For any w, we
can write it as the sum of w1+w2, where w1 is perpendicular to v, and w2 is in the
same direction as v. So v*w1 = 0. v*w2 = ||w2||, since v*w2/||w2|| = 1. Then, if we just
draw a picture, we can see that cos alpha = ||w2|| = v*w2 = v*w.
Matrices
   Sum:




   A and B must have the same
   dimensions
                   Matrices
Product:
                      A and B must have
                      compatible dimensions




Identity Matrix:
             Matrices
Transpose:




       If       A is symmetric
Indexing into matrices
Files

Matlab
                Functions
• Format: function o = test(x,y)
• Name function and file the same.
• Only first function in file is visible
  outside the file.
• Look at sample function
                 Images
•   Black and white image is a 2D matrix.
•   Intensities represented as pixels.
•   Color images are 3D matrix, RBG.
•   Matlab
             Debugging
• Add print statements to function by
  leaving off ;
• keyboard
• debug and breakpoint
            Conclusions
• Quick tour of matlab, you should teach
  yourself the rest. We’ll give hints in
  problem sets.
• The inner product will be very important.

				
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posted:5/5/2011
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