Finite-Dimensional Vector Spaces

1. Front Matter

   Pages i-viii

   PDF

2. Spaces

   • Paul R. Halmos

   Pages 1-54

3. Transformations

   • Paul R. Halmos

   Pages 55-117

4. Orthogonality

   • Paul R. Halmos

   Pages 118-174

5. Analysis

   • Paul R. Halmos

   Pages 175-188

6. Back Matter

   Pages 189-200

   PDF

“The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other “modern” textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher.” Zentralblatt für Mathematik

• Endlichdimensionaler Vektorraum
• Finite
• Morphism
• Parity
• Permutation
• Transformation
• Vector
• calculus
• function
• mathematics
• theorem

“This is a classic but still useful introduction to modern linear algebra. It is primarily about linear transformations … . It’s also extremely well-written and logical, with short and elegant proofs. … The exercises are very good, and are a mixture of proof questions and concrete examples. The book ends with a few applications to analysis … and a brief summary of what is needed to extend this theory to Hilbert spaces.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)

“The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity. The presentation is never awkward or dry, as it sometimes is in other “modern” textbooks; it is as unconventional as one has come to expect from the author. The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher.” Zentralblatt für Mathematik

• Department of Mathematics, Santa Clara University, Santa Clara, USA

  Paul R. Halmos

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