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WildLinAlg6: Applications of 2x2 matrices

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Uploaded on Mar 8, 2011

This is the 6th lecture in this course on Linear Algebra. We review matrix arithmetic for 2x2 matrices and compare the main laws with the simpler case of 1x1 matrices. Then we apply 2x2 matrices to study transformations of vectors, with examples including reflections, rotations and dilations.

We visualize these with pictures using the standard Cartesian coordinate framework. The concept of a linear transformation is also introduced.

This is part of a series on Linear Algebra given by N J Wildberger, also the discoverer of Rational Trigonometry.

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  1. 1

    WildLinAlg1: Introduction to Linear Algebra (N J Wildberger)

  2. 2

    WildLinAlg2: Geometry with vectors

  3. 3

    WildLinAlg3: Center of mass and barycentric coordinates

  4. 4

    WildLinAlg4: Area and volume

  5. 5

    WildLinAlg5: Change of coordinates and determinants

  6. WildLinAlg6: Applications of 2x2 matrices

  7. 7

    WildLinAlg7: More applications of 2x2 matrices

  8. 8

    WildLinAlg8: Inverting 3x3 matrices

  9. 9

    WildLinAlg9: Three dimensional affine geometry

  10. 10

    WildLinAlg10: Equations of lines and planes in 3D

  11. 11

    WildLinAlg11: Applications of 3x3 matrices

  12. 12

    WildLinAlg12: Generalized dilations and eigenvalues

  13. 13

    WildLinAlg13: Solving a system of linear equations

  14. 14

    WildLinAlg14: More row reduction with parameters

  15. 15

    WildLinAlg15: Applications of row reduction (Gaussian elimination) I

  16. 16

    WildLinAlg16: Applications of row reduction II

  17. 17

    WildLinAlg17: Rank and Nullity of a Linear Transformation

  18. 18

    WildLinAlg18: The geometry of a system of linear equations

  19. 19

    WildLinAlg19: Linear algebra with polynomials

  20. 20

    WildLinAlg20: Bases of polynomial spaces

  21. 21

    WildLinAlg21: More bases of polynomial spaces

  22. 22

    WildLinAlg22: Polynomials and sequence spaces

  23. 23

    WildLinAlg23: Stirling numbers and Pascal triangles

  24. 24

    WildLinAlg24: Cubic splines (Bezier curves) using linear algebra

  25. 25

    WildLinAlg25: Cubic splines using calculus

  26. 26

    WildLinAlg26: Change of basis and Taylor coefficient vectors

  27. 27

    WildLinAlg27: Geometry with linear algebra

  28. 28

    WildLinAlg28: Dot products, Pythagoras' theorem, and generalizations

  29. 29

    WildLinAlg29: Applications of the dot product to planar geometry I

  30. 30

    WildLinAlg30: Applications of the dot product to planar geometry II

  31. 31

    WildLinAlg31: Circles and spheres via dot products I

  32. 32

    WildLinAlg32: Circles and spheres via dot products II

  33. 33

    WildLinAlg33: The relativistic dot product

  34. 34

    WildLinAlg34: Oriented circles and 3D relativistic geometry I

  35. 35

    WildLinAlg35: Oriented circles and relativistic geometry II

  36. 36

    WildLinAlg36: Energy, momentum and linear algebra

  37. 37

    WildLinAlg37: An elementary introduction to Special Relativity I

  38. 38

    WildLinAlg38: An elementary introduction to Special Relativity II

  39. 39

    WildLinAlg39: Length contraction, time dilation and velocity addition

  40. 40

    WildLinAlg40a: Relativistic dot products and complex numbers

  41. 41

    WildLinAlg40b: Relativistic dot products and complex numbers II

  42. 42

    WildLinAlg41: The chromatic algebra of 2x2 matrices I

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