11725410
Descripción
Mapa Mental por Ruby Kalra, actualizado hace más de 1 año
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Creado por Ruby Kalra
hace alrededor de 7 años
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131: MathematicalSpaces
- Linear Spaces
(Vector Spaces)
- Vector Subspaces
- contain elements
- infinite dimensional
- functions
- real
- defining
properties
- defining
properties
- complex
- real
- functions
- 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)
- Vector Projection; Observe
"overlap degree" of two vector
quantities
- Einstein Summation Notation
- Cross Product
- Levi-Civita Notation
- Levi-Civita
(Permutation)
Symbol
- E123=1
- Antisymmetric
(swap sign per
each index swap)
- E123=1
- Levi-Civita
(Permutation)
Symbol
- Algebraic Notation
- Intuition
- Defines Perpendicular
Vector ("area of plane"
vector)
- Defines Perpendicular
Vector ("area of plane"
vector)
- Levi-Civita Notation
- Dot Product
- Three Vectors
- Triple Scalar Product
(cyclically permutable)
- Defines 3-D Volume (3-D
Determinant)
- Defines 3-D Volume (3-D
Determinant)
- Triple Vector Product
(obeys cyclic permutation)
- Triple Scalar Product
(cyclically permutable)
- Scaling
- Vector Addition
- Component by
Component
- Component by
Component
- Vector
Multiplication
- Vector Algebra
- closed under vector addition
and scalar multiplication
(linear combination)
- defining
properties
- mathematically represent models of
multi-element physical systems
- real
- matrices (nxn
or nxm)
- vectors
- infinite dimensional
- Vector Subspaces
- Topological Spaces
- Hilbert Spaces
- others
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