Finite-Dimensional Vector Spaces by Halmos

[micromass]

• Author: Paul Halmos
• Title: Finite-Dimensional Vector Spaces
• Amazon Link: https://www.amazon.com/dp/0387900934/?tag=pfamazon01-20

 

[mathwonk]

This is a good solid book, by an expert on Hilbert spaces, whose goal was to present finite dimensional vector space theory as the easy case of Hilbert space theory. The book was written back before really good sophisticated type setting software came in vogue, so the material is crowded and crammed on the page in a way that can make it hard to read. Just look at the table of contents to see what I mean. The different topics are all run together in a single paragraph instead of being decently spread out for better display.

The discussion is more in words than symbols as well, not lengthy, but demanding good reading comprehension skills. The proofs are also intelligently written and demanding close attention. So the mathematics is excellent, but may be best appreciated by someone who already knows a good bit of the material. I benefited from it when teaching advanced linear algebra. He made some things clearer to me that I thought I already knew, and pointed out some aspects I had not known, because he understands them so well.

So for many of us probably a second book on the topic, as is Axler.