Reddit mentions of A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)

same here. In the rush to get everyone ok with matrix arithmetic, I feel like most students never realized that the matrix was just a nifty way to do bookkeeping. And it's not a bad thing; it's a great tool to use and if you're on the STE side of STEM majors there might not be a lot of reason to go above it. But it does make for a wild transition when/if you ever go up a level in abstraction.

I, for example, had no idea at all. Then I was helping a friend with some programming and we stumbled onto quaternions for 6DoF modeling. Talk about a 180. I feel like I'm still re-wiring all of my algebraic understanding from that point backwards. This book was fun to read when I made that turn too.

to me, the most interesting mathematical history books are those with a targeted goal, meaning they cover the historical aspect of a specific topic, time period, person or group of people, etc. these, at least in my opinion, provide the most insight, as some of the more general books, particular those written for the general public, are too overarching to get much out of. also, another suggestion is to find biographies of mathematicians or physicists. i personally do not find any math history prior to the 1500-1600s or so that interesting, so all of my suggestions are appropriately biased.

a few suggestions are:

• a history of vector analysis by michael j. crowe
  
• isaac newton by james gleick
  
• isaac newton by gale e. christianson
  
• the clockwork universe: isaac newton, the royal society, and the birth of the modern world
  
• gravity by george gamow
  
• one two three ... infinity by george gamow
  
• the mactutor history of mathematics archive - the biographies index is really pretty good and is often a starting point for me.
  
• ams notices - great for finding expository articles and interviews
  
  i don't know of many books that follow the history of a certain subject that are any good. most of my historical knowledge regarding a certain subject is taken from multiple sources. a good method is to read articles, track down the books and/or papers that are referenced by a certain book or paper you like, find biographies of the mathematicians involved, etc. for instance, interviews with mathematicians (like those in the ams notices and the one i posted the other day) are fantastic troves of information regarding the history of certain topics, because the story is being told by a direct participant.