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11725410
131: MathematicalSpaces
Descrição
mind map of 131 concepts for fall 17 final
Sem etiquetas
131
fall 2017
mind map
physics
math
linear algebra
physics
Mapa Mental por
Ruby Kalra
, atualizado more than 1 year ago
Mais
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Criado por
Ruby Kalra
quase 7 anos atrás
20
0
0
Resumo de Recurso
131: MathematicalSpaces
Linear Spaces (Vector Spaces)
Vector Subspaces
contain elements
infinite dimensional
functions
real
defining properties
complex
finite dimensional
vectors
real
complex
defining properties
closed under vector addition and scalar multiplication (linear combination)
Interaction
Vector Algebra
Vector Multiplication
Scaling
Two Vectors
Dot Product
Einstein Summation Notation
Algebraic Notation
Intuition
Vector Projection; Observe "overlap degree" of two vector quantities
small-scale operation (vector-on-vector)
Cross Product
Levi-Civita Notation
Levi-Civita (Permutation) Symbol
E123=1
Antisymmetric (swap sign per each index swap)
Algebraic Notation
Intuition
Defines Perpendicular Vector ("area of plane" vector)
Three Vectors
Triple Scalar Product (cyclically permutable)
Defines 3-D Volume (3-D Determinant)
Triple Vector Product (obeys cyclic permutation)
Vector Addition
Component by Component
mathematically represent models of multi-element physical systems
matrices (nxn or nxm)
Topological Spaces
Hilbert Spaces
others
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