Why no Halmos, "Finite-dimensional vector spaces"? It's pretty theoretical but very approachable also. I own that book and have worked through a few chapters. It is one of the first linear algebra books in a "modern" style, being published in The reason it's not on the list is I just didn't see what it had to offer that isn't covered in later books. Happy to be convinced otherwise though.
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As a newly minted Ph. He eventually became John von Neumann's research assistant, and it was one 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 discuss the three-dimensional area where vectors can be plotted. The book broke ground as the first formal introduction to linear algebra, a branch of modern 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 flow, electronic circuits, and population genetics.
In Halmos received the coveted Steele Prize for exposition from the American Mathematical Society for "his many graduate texts in mathematics dealing with finite dimensional vector spaces, measure theory, ergodic theory, and Hilbert space. Finite Dimensional Vector Spaces. Paul R. U Definition of linear dependence. Nonlinear Programming Olvi L.
Finite-Dimensional Vector Spaces
This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations, and despite the title most of the theorems and proofs work for arbitrary vector spaces. The book does start from the beginning and assumes no prior knowledge of the subject. But it has no pictures, no worked examples, no discussion of algorithms or numerical methods, and very little motivation.
Finite Dimensional Vector Spaces. (AM-7), Volume 7
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