Linear Algebra and Group Theory for Physicists and Engineers

Part I: Introduction to Linear Algebra.- Vectors and Matrices.- Determinant and Vector Product in Physics.- Markov Matrix and its Spectrum: Towards Search Engines.- Special Relativity: Algebraic Point of View.- Part II: Introduction to Group Theory.- Groups and Isomorphism Theorems.- Projective Geometry in Computer Graphics.- Quantum Mechanics: Algebraic Point of View.- Part III: Polynomials and Basis Functions.- Polynomials and Their Gradient.- Basis Functions: Barycentric Coordinates in 3D.- Part IV: Finite Elements in 3-D. - Automatic Mesh Generation.- Mesh Regularity.- Numerical Integration.- Spline: Variational Model in 3D.- Part V: Permuation Group in Quantum Chemistry.- Determinant and Electronic Structure.- Part VI: The Jordan Form.- The Jordan Form.- Jordan Decomposition.- Algebras and their Derivation.- Part VII: Linearization in Numerical Relativity.- Einstein Equations and their Linearization.

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• Teoria matemática da computação
• Álgebra
• Física Matemática
• Grupos e teoria do grupo
• Análise numérica

Group theory;Linear algebra;High dimensional vectors;Fourier matrices;Markov chain;Quantum mechanics;Mesh generation;matrix theory;Jordan form;Jordan decomposition