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PR414 / PR813  Background
Lecture 0   




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Purpose: Reviewing elementary linear algebra and probability theory concepts

Material: Strang (or similar) for linear algebra, Peebles and/or Leon-Garcia (or similar) for probability theory.

Task: Review the following concepts (which you should have covered in prior courses):

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What is orthogonal and orthonormal bases.
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How do you invert an orthonormal matrix by means of its transposed?
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How do you use dot-products to express/project vector data in terms of an alternative axis system?
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Review the eigenvalue and SVD problems. Can you express it fully in terms of matrixes?
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Review the multi-dimentional Gaussian pdf:
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Do you understand the interpretation of the 2 sets of paramaters (mean-vector and covariance matrix)?
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Play with this expression to get a feel for its behaviour. For instance, create a 2-dimensional Gaussian pdf (to your taste) and evaluate and plot its height for a grid of data. Make sure you understand the role of its parameters. How will you approach dimensions higher than 2?




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Johan du Preez 2005-02-09