Task and Mark distribution:
This Individual Coursework involves investigating properties of orthogonal matrices, the bivariate normal distribution, and investigating some of the links between them using small examples involving numpy and matplotlib. You are encouraged to explore the topic, use your initiative, and show some originality, within the time available. Ensure that you clearly reference any sources you have used. Please submit one report (e.g. as a single Microsoft Word document) covering all of the tasks below, clearly organised by task. Make sure you include your Python code and selected output directly in the report. You must not submit a zip file. The word limit is a maximum rather than a target. Concentrate on producing a clear and concise answer to each task.
A square matrix ? is called orthogonal if ??? = ?.
(1) Suppose ? is an ? × ? orthogonal matrix. Describe what properties the columns of ? have,
and what properties of vectors are preserved when ? is used as a matrix transformation.
Illustrate (or check) these properties with small 2D and 3D examples using numpy.
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