Linear algebra from a historical perspective?

In summary, the conversation is about the search for non-technical historical accounts or introductory books on linear algebra that develop the basic ideas in the order they were developed. Suggestions for such books include "A History of Vector Analysis" by Crowe, "The Theory of Determinants in the Historical Order of Development" by Sir Thomas Muir, and a paper from the Michigan Historical Reprint Series. The conversation also mentions a potentially useful article from ScienceDirect, which has not yet been read but is considered promising due to its recent publication and potential references to previous works on the subject.
  • #1
math5434
2
0
Hi all,

I am looking for either (or both) a non-technical historical account of linear algebra (the closest I've found is Crowe's "A History of Vector Analysis") or an introductory (first course) book that develops the basic ideas in roughly the order they were developed. Do such books exist?
 
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  • #3
Thanks! Anyone else? It's surprising there is not a more extensive treatment of the historical development of linear algebra. I would think it would be a popular read.
 
  • #4
The theory of determinants in the historical order of development, by Sir Thomas Muir. 3vols I think (Paperback)
~ Michigan Historical Reprint Series (Author) "THE number of writings to be considered under this heading amounts to about one hundred and eighty (180), and the number of writers to about..."
 
  • #5
here's another one I've stumbled on
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6WG9-45NJHDR-D&_user=10&_coverDate=12%2F31%2F1995&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=190a5d1659e04624a4da353b06a4cb11

haven't read it yet, but i would say it's good because it's relatively recent so it would reference a lot of stuff on the subject that has come before it
 

1. What is the origin of linear algebra?

The origins of linear algebra can be traced back to ancient civilizations such as Babylonia and Egypt, where systems of linear equations were used to solve practical problems related to land division, taxation, and commerce. However, the modern form of linear algebra emerged in the 17th century with the work of mathematicians like René Descartes and Isaac Newton.

2. Who were the key figures in the development of linear algebra?

Some of the key figures in the development of linear algebra include Gauss, who developed the method of least squares and introduced the concept of a matrix; Cayley, who formalized the algebra of matrices; and Jordan, who introduced the concept of a linear transformation. Other important contributors include Hermann Grassmann, Arthur Cayley, and Évariste Galois.

3. How did linear algebra contribute to the development of other branches of mathematics?

Linear algebra has played a crucial role in the development of other branches of mathematics such as abstract algebra, geometry, and calculus. The concept of a vector space, which is central to linear algebra, has been extended to more abstract spaces in abstract algebra. The use of matrices has also been incorporated into differential geometry and multivariate calculus.

4. What are some important applications of linear algebra?

Linear algebra has a wide range of applications in various fields such as physics, engineering, computer science, and economics. Some common applications include solving systems of linear equations, data analysis, optimization problems, image processing, and machine learning.

5. How has the study of linear algebra evolved over time?

The study of linear algebra has evolved significantly over time, from its early origins in ancient civilizations to its modern form. With the advent of computers, the use of linear algebra has become even more widespread, with the development of algorithms for solving large systems of equations and applications in fields such as data science and artificial intelligence.

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