# Tutorial

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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:
/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

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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