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Book Review: Matrix Analysis and Applied Linear Algebra, 2nd Edition

When I discovered the first edition of Carl D. Meyer’s book on “Matrix Analysis and Applied Linear Algebra”, I considered it the best book on Linear Algebra I was aware of — and surely the best available book for an application-minded reader. In short: the book I really wished had been available when I was a graduate student and encountering this material for the first time.

So it was with great excitement and curiosity when I saw that a new, second edition was available. How could a near-perfect book be made even better?

The Irrationality of e

The proof that $\sqrt{2}$ is irrational is part of the standard high-school curriculum. The same cannot be said for the proof that $e$, the base of the natural logarithm, is irrational as well. Yet the proof is short, simple, elegant.

Ein literarisches Portrait Bernhard von Lepels?

Bernhard von Lepel ist für uns hauptsächlich interessant durch seine Freundschaft mit Theodor Fontane, und das meiste, das wir über ihn wissen, wissen wir durch Fontane. Fontane hat dem Freund ein langes Kapitel in seinen Jugenderinnerungen (Kapitel 8 von “Der Tunnel über der Spree” in “Von 20 bis 30”) gewidmet, und ihn auch sonst gelegentlich beschrieben — seltsamerweise zum Teil verfremdet (z.B. als der “Italienenthusiast” in der etwas mysteriösen Skizze “Cafés von heut und Konditoreien von ehmals” von 1886). Dennoch bleibt Lepel’s Persönlichkeit überraschend undeutlich.

An Intuitive Explanation for the Birthday Paradox

The so-called “birthday paradox” concerns the fact that even in surprisingly small groups the probability for at least two people to share their birthdate is surprisingly high.

The combinatorics of the Birthday Paradox are not hard; in fact, it is a standard example in introductory textbooks. Yet, the typical exact treatment provides no intuitive sense for the way the probability depends on the size of the sample and the population.

Here is an approximate solution that shows that the probability in question is, in fact, a Gaussian.

Go is Weird: Strings

Having done extensive programming in C, I am not particularly spoiled when it comes to idiosyncrasies of a language’s “string” type. Yet, Go’s string types keeps tripping me up — why does it all still have to be that complicated?