Linear Algebra and Analytic Geometry for Physical Sciences [electronic resource] by Giovanni Landi, Alessandro Zampini.

A self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physic...

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Bibliographic Details
Uniform Title:Undergraduate Lecture Notes in Physics, 2192-4805
Main Authors: Landi, Giovanni (Author)
Zampini, Alessandro (Author)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
Edition:1st ed. 2018.
Series:Undergraduate Lecture Notes in Physics,
Subjects:
Mathematical physics.
Algebras, Linear.
Engineering mathematics.
Engineering—Data processing.
Geometry.
Computer science—Mathematics.
Online Access:
Springer Physics and Astronomy eBooks 2018 English/International: 2018 (Springer Link)
Format: Electronic eBook
Contents:
  • Introduction
  • Vectors and coordinate systems
  • Vector spaces
  • Euclidean vector spaces
  • Matrices
  • The determinant
  • Systems of linear equations
  • Linear transformations
  • Dual spaces
  • Endomorphisms and diagonalization
  • Spectral theorems on euclidean spaces
  • Rotations
  • Spectral theorems on hermitian spaces
  • Quadratic forms
  • Affine linear geometry
  • Euclidean affine linear geometry
  • Conic sections
  • A Algebraic Structures
  • A.1 A few notions of Set Theory
  • A.2 Groups
  • A.3 Rings and Fields
  • A.4 Maps between algebraic structures
  • A5 Complex numbers
  • A.6 Integers modulo a prime number.