I agree- this is a great textbook for graduate students in computer science, but it is utterly unsuitable for the typical freshmen/sophomore level discrete math course for CS majors.

The whitening transformation described in the Wikipedia article that you linked to assumes that you have a random vector with a known covariance structure. By "the projection is conditional expectation with respect to the $\sigma$ algebra generated by the RV's already processed" it would seem that you're referring to some kind of process in which $\Sigma$ is dynamically updated. Could you be more specific about what you're referring to here?

What background in mathematics do your students have? In particular, have they done any proofed based mathematics courses? You need to be realistic about how much you'll actually be able to teach them.

The definition of "dual norm" used in this question isn't at all standard. The standard definition is that $\| y \|_{*}=\sup \left\{ y^{T}x | \| x \| \leq 1 \right\} $

Mark- I believe that $r$ is uniformly distributed over the surface of the hypersphere. The answer to the question will change dramatically if it isn't.

Also note that it really doesn't matter where $v_{i}$ comes from. The question you want to answer is "Given a fixed vector $x$ and random vector $r$, what is $P(|r^{T}x| < \alpha)$?"

Note that using the rand() function in MATLAB to generate your $r$ vector won't generate a vector uniformly distributed over the surface of the unit ball- you want to use randn().

Do you really want $x$ be to the value of $a$ that minimizes $\max_{\lambda \in \Lambda} | R(h\lambda) |$, or do you want $x$ to be the minimal objective value?

This iteration is a simple version of what is called "the method of multipliers" in optimization. Its convergence isn't robust, but can be improved by using an augmented Lagrangian to stabilize the algorithm.

For problems of that size, you'll definitely want to look at first order methods such as the alternating direction method of multipliers.

$S$ is a linear operator, so you can take the factors of $1/m$ out of $S(l/m)$ and rewrite your constraint as $L-\frac{1}{m} S(l)^{T}S(l) \succ 0$

It should also be clear that you can add any vector in $N(A)$ to $x_{m}$ to get another least squares solution. Thus if $N(A)$ is nontrivial, then the set of least square squares solutions is unbounded.

Alexander- this is an important property of the pseudoinverse solution that can be found in many textbooks. For example, it's in Strang's "Linear Algebra and its Applications." There isn't room in this comment for a complete proof, but the key point is that any least squares solution $x_{LS}$ can be written uniquely as $x_{LS}=x_{m}+x_{n}$, where $x_{m}$ (the pseudoinverse inverse solution) is in $R(A^{T})$ and $x_{n}$ is in $N(A)$. Since $N(A) \perp R(A^{T})$, $\| x_{LS} \|^{2}=\| x_{m} \|^{2}+ \| x_{n} \|^{2}$, and $\| x_{LS} \|$ is minimized when $x_{n}=0$.