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单词 TopicsOnVectors
释义

topics on vectors


I Vector algebra

  1. 1.

    definition of vector

  2. 2.

    vector spaceMathworldPlanetmath

  3. 3.

    parallelogram principle, median vector, difference of vectors

  4. 4.

    geometric applications: mid-segment theorem, common point of triangle medians, median of trapezoid

  5. 5.

    system of coordinatesMathworldPlanetmathPlanetmath

  6. 6.

    basis

  7. 7.

    coordinate vector

  8. 8.

    position vector

  9. 9.

    norm (http://planetmath.org/VectorPNorm) (through Pythagoras)

  10. 10.

    unit vectorMathworldPlanetmath

  11. 11.

    direction cosinesMathworldPlanetmath

  12. 12.

    dot productMathworldPlanetmath

  13. 13.

    http://planetmath.org/node/6178parallelismPlanetmathPlanetmathPlanetmath condition

  14. 14.

    http://planetmath.org/node/6178orthogonality condition

  15. 15.

    vector components and scalar components

  16. 16.

    cross productMathworldPlanetmath

  17. 17.

    area (http://planetmath.org/CrossProduct) of parallelogramMathworldPlanetmath

  18. 18.

    triple scalar product, volume of prism

  19. 19.

    triple cross product

  20. 20.

    distance of non-parallel lines (an application)

  21. 21.

    matrices and determinantsMathworldPlanetmath

  22. 22.

    matrices and linear mappings

  23. 23.

    linear systems and solution methods

II Vector calculus

  1. 1.

    definiton of real valued vector function

  2. 2.

    derivative of vector function

  3. 3.

    properties of derivative of vector function

  4. 4.

    derivative of a vector function with constant norm

  5. 5.

    nabla

  6. 6.

    cylindrical coordinatesMathworldPlanetmath

  7. 7.

    polar coordinates

  8. 8.

    spherical coordinatesMathworldPlanetmath

  9. 9.

    differential geometryMathworldPlanetmath (http://planetmath.org/ClassicalDifferentialGeometry)

  10. 10.

    tangentMathworldPlanetmathPlanetmathPlanetmath (http://planetmath.org/TangentSpace), normal (http://planetmath.org/NormalVector) and binormal vectors

  11. 11.

    osculating planeMathworldPlanetmath, normal planeMathworldPlanetmath and binormal planes

  12. 12.

    Frenet frame

  13. 13.

    Frenet-Serret equations

  14. 14.

    kinematic method for calculating the radius of curvatureMathworldPlanetmath (http://planetmath.org/CurvatureOfACurve)

  15. 15.

    gradientMathworldPlanetmath of a scalar function

  16. 16.

    divergenceMathworldPlanetmath of a vector function

  17. 17.

    solenoidal fieldMathworldPlanetmath

  18. 18.

    vector potentialMathworldPlanetmath

  19. 19.

    curl of a vector function

  20. 20.

    irrotational fieldMathworldPlanetmath, lamellar field

  21. 21.

    Helmholtz decomposition

  22. 22.

    integration of vector functions

  23. 23.

    line integralMathworldPlanetmath

  24. 24.

    tensors and differential forms

  25. 25.

    covariant differentiation

III Integral theorems

  1. 1.

    Gauss theorem

  2. 2.

    solid angle

  3. 3.

    Green theoremsMathworldPlanetmath

  4. 4.

    Stokes theorem

  5. 5.

    circulation and vorticity

  6. 6.

    Kelvin theorem

  7. 7.

    Helmholtz theorems

IV Vector advanced topics

  1. 1.

    alternate characterization of curl

  2. 2.

    tensor notation for a vector

  3. 3.

    transformation law for a vector

  4. 4.

    vector fieldsMathworldPlanetmath: Lagrangian and Eulerian description

  5. 5.

    motion of continuum

  6. 6.

    JacobiansMathworldPlanetmathPlanetmath connected with transformation of integration regions

  7. 7.

    Reynolds transport theoremMathworldPlanetmath

  8. 8.

    rotationsMathworldPlanetmath

  9. 9.

    linear transformation spaces

  10. 10.

    linear functionalsMathworldPlanetmath or covectors

  11. 11.

    bivectors

  12. 12.

    exterior or Grassmann algebra

  13. 13.

    Clifford algebraMathworldPlanetmathPlanetmath

  14. 14.

    quaternions

  15. 15.

    projective geometry

  16. 16.

    Grassmann-Cayley algebra

  17. 17.

    vector bundles

  18. 18.

    connectionsMathworldPlanetmath

  19. 19.

    spinors

  20. 20.

    twistors

  21. 21.

    spin structures

  22. 22.

    linear programming and the simplex method

  23. 23.

    representation theory

  24. 24.

    linear extension

  25. 25.

    K-theory

  26. 26.

    Category Vect

V Endomorphism decomposition

  1. 1.

    eigenvaluesMathworldPlanetmathPlanetmathPlanetmathPlanetmath, eigenvectorsMathworldPlanetmathPlanetmathPlanetmath

  2. 2.

    characteristicPlanetmathPlanetmath and minimal polynomialsPlanetmathPlanetmath

  3. 3.

    eigen-subspaces and invariant subspaces

  4. 4.

    Hamilton-Cayley theorem (http://planetmath.org/CayleyHamiltonTheorem)

  5. 5.

    Jordan blocksMathworldPlanetmath and canonical decomposition

  6. 6.

    singular value decompositionMathworldPlanetmath

VI Lie groups and Lie algebras

  1. 1.

    the connection between Lie groups and Lie algebras

  2. 2.

    commutators or Lie bracket

  3. 3.

    matrix groups and algebras

  4. 4.

    Pauli matricesMathworldPlanetmath

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