coding the matrix week1 introduction 2

A comprehension is an expression, that produces a set, a list, or a dictionary.It's very concise, but also easy to read, as long as you're used to it.

A comprehension syntactically resembles the notation used by mathematicians, to write down sets.

Perhaps most important for our purposes, a comprehension allows you to write a procedure, with only a single line without sacrificing readability.

My main bit of advice, try stuff out, my intention is that you be empowered to work with vectors and matrices and the algorithms that operate on them.

I'm giving you the tools, but you have to take the initiative.

My second bit of advice is, unfortunately you're going to have to do a little bit of memorization.In particular, in the early part of the course we'll discuss difference interpretations of matrix-vector, vector-matrix and matrix-matrix multiplication. You need to, really learn these interpretations in order to even understand the lectures that come afterwards.

Now a word about proofs, mathematical statements, lemmas, propositions, theorems, are an essential part of linear algebra. They underlie the concepts that we use.

In this course, I present proofs for most of the theorems relevant to the topics we discuss.

If you don't consider yourself mathematically inclined, you might be tempted to just skip the proofs. That would be a mistake, mathematical proofs are not there just to convince, but to provide insight. The best kind of proof helps us understand why a theorem is true.

Working through the proof, trying to understand its steps, helps us understand the meaning of the theorem and also helps us learn the theorem. Since I'm a coder, I tend to think of things algorithmically or procedurally.Sometimes, I'll ask you to code a procedure that follows the structure of the proof.

The resulting procedure is not generally the most practical way to solve the problem, but it will help you gain insight into the proof.

For one thing, that would require a deep knowledge of numerical analysis. Which is at least in part, the ability of numerical algorithms to tolerate round-off error.

The methods I teach are a compromise between, on the one hand, efficiency and accuracy and, on the other hand, pedagogical value.

Your performance on quizzes doesn't enter into your grade, but you will be expected to know and understand the answers to all the quizzes.