Linear Algebra and Analytic Geometry for Physical Sciences

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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Hlavní autor: Landi, Giovanni (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Cham : Springer International Publishing, 2018.
Vydání:1st ed. 2018.
Edice:Undergraduate Lecture Notes in Physics,
Témata:
Physics.
Matrix theory.
Algebra.
Applied mathematics.
Engineering mathematics.
Geometry.
Computer science-Mathematics.
Mathematical physics.
ISBN:9783319783611
ISSN:2192-4791
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Obsah:
  • 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.

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