Copy and Edit

131: MathematicalSpaces

Description

mind map of 131 concepts for fall 17 final
Ruby Kalra
Mind Map by Ruby Kalra, updated more than 1 year ago
Ruby Kalra
Created by Ruby Kalra almost 7 years ago
20
0
0

Resource summary

131: MathematicalSpaces
  1. Linear Spaces (Vector Spaces)
    1. Vector Subspaces
      1. contain elements
        1. infinite dimensional
          1. functions
            1. real
              1. defining properties
              2. complex
            2. finite dimensional
              1. vectors
                1. real
                  2. complex
                    1. defining properties
                      1. closed under vector addition and scalar multiplication (linear combination)
                        1. Interaction
                          1. Vector Algebra
                            1. Vector Multiplication
                              1. Scaling
                                1. Two Vectors
                                  1. Dot Product
                                    1. Einstein Summation Notation
                                      1. Algebraic Notation
                                        1. Intuition
                                          1. Vector Projection; Observe "overlap degree" of two vector quantities
                                            1. small-scale operation (vector-on-vector)
                                          2. Cross Product
                                            1. Levi-Civita Notation
                                              1. Levi-Civita (Permutation) Symbol
                                                1. E123=1
                                                  1. Antisymmetric (swap sign per each index swap)
                                                2. Algebraic Notation
                                                  1. Intuition
                                                    1. Defines Perpendicular Vector ("area of plane" vector)
                                                3. Three Vectors
                                                  1. Triple Scalar Product (cyclically permutable)
                                                    1. Defines 3-D Volume (3-D Determinant)
                                                    2. Triple Vector Product (obeys cyclic permutation)
                                                  2. Vector Addition
                                                    1. Component by Component
                                            2. mathematically represent models of multi-element physical systems
                                            3. matrices (nxn or nxm)
                                        2. Topological Spaces
                                          1. Hilbert Spaces
                                            1. others
                                              Show full summary Hide full summary

                                              Want to create your own Mind Maps for free with GoConqr? Learn more.

                                              Similar

                                              Pythagorean Theorem Quiz
                                              Selam H
                                              GCSE AQA Physics - Unit 3
                                              James Jolliffe
                                              AQA Physics P1 Quiz
                                              Bella Statham
                                              Using GoConqr to study science
                                              Sarah Egan
                                              GCSE AQA Physics 1 Energy & Efficiency
                                              Lilac Potato
                                              Waves
                                              kate.siena
                                              Geometry Vocabulary
                                              patticlj
                                              Forces and their effects
                                              kate.siena
                                              Forces and motion
                                              Catarina Borges
                                              Junior Cert Physics formulas
                                              Sarah Egan
                                              OCR Physics P4 Revision
                                              Dan Allibone
                                              Browse Library