Hamburger, H. L. — Linear Transformations in N-Dimensional Vector Space; an Introduction to the Theory of Hilbert Space, by H.L. Hamburger and M.E. Grimshaw

Cambridge [Eng.], University Press, 1951. Hardcover. vii, 195 p. 23 cm. Good condition Linear Transformations in n-Dimensional Vector Space introduces readers to the theoretical framework of Hilbert spaces, which are central to many areas of mathematics and physics, particularly quantum mechanics. The treatment of Hilbert spaces in this book likely emphasizes their properties, structure, and applications, making it an important resource for mathematicians and physicists in the mid-20th century as the theory of Hilbert spaces was still being developed and refined. The book focuses on linear transformations in finite-dimensional vector spaces, a fundamental concept in linear algebra. The understanding of these transformations serves as a stepping stone to more abstract concepts like operators on infinite-dimensional spaces, which are central to the theory of Hilbert spaces.The theory of Hilbert spaces is indispensable in many fields, such as quantum mechanics, signal processing, and functional analysis. This book serves as a bridge between linear algebra and the more abstract and general concepts in functional analysis, which were being actively developed during the early 20th century.