Notebook 3

Questions Answers

Goals

• Introduction to linear algebra! A topic that is fundamental and you will encounter repeatedly on your journey. This week (long as it is) is just the start!

Resources

• This is one of the most important notebooks. Even if you’ve done some linear algebra before, pay attention. Hopefully some things will be explained in a novel way to you.
• A great course on linear algebra is by 3blue1brown. You could go through it (excepting the sections on cross-products and Cramer’s rule). This would put you in a great position for the rest of the module.
• Another good ‘standard’ course is by Gil Strang.

Challenging, skippable questions

(think of these questions as useful practice rather than core content)

• The questions on building clocks
• The question box about polynomials
• The example on linear image transformations, and all the associated questions.
• The question box on the equivalence between abstract linear maps and matrices. It starts : These questions assume vector spaces U…

Ensure you’re happy with these concepts

• Understanding the dimensionality of tensors, and how to create (e.g. a 4d-tensor) Understanding the following concepts:
• Vector spaces, the span of a vector space, the basis of a vector space
• Linear dependence of a vector on other vectors
• Matrix multiplication
• The concept of a linear transformation and its properties
• Programming techniques seen in the answers. Particularly list comprehensions.

Credits

• Thanks to Giuseppe Castiglione for giving excellent feedback and checking the notebook..
• Thanks to Giuseppe Castiglione for adding answers to the questions.