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Finite Dimensional Vector Spaces

2012 Reprint of 1942 Edition. Exact facsimile of the original edition, not reproduced with Optical Recognition Software. As a newly minted Ph.D., Paul Halmos came to the Institute for Advanced Study in 1938–although he did not have a fellowship–to study some of the many giants of mathematics who had recently joined the faculty. He in the end became John von Neumann’s research assistant, and it used to be one in every of von Neumann’s inspiring lectures that spurred Halmos to write “Finite Dimensional Vector Spaces.” The book brought him instant fame as an expositor of mathematics. Finite Dimensional Vector Spaces combines algebra and geometry to speak about the three-dimensional area where vectors will also be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of brand new mathematics that studies vectors and vector spaces. The book continues to exert its influence sixty years after publication, as linear algebra is now widely used, not only in mathematics but also in the natural and social sciences, for studying such subjects as weather problems, traffic drift, electronic circuits, and population genetics. In 1983 Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for “his many graduate texts in mathematics coping with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space.”

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