Linear Algebra

  1. Linear Transformations
    1. Introduction to Linear Transformations
      1. Definition and linearity conditions
        1. Domain and codomain
          1. Linear transformations from Rⁿ to Rᵐ
            1. Geometric transformations in R²
              1. Rotations
                1. Reflections
                  1. Projections
                    1. Scaling transformations
                      1. Shear transformations
                      2. Composition of transformations
                        1. Identity and inverse transformations
                        2. Kernel and Image
                          1. Kernel of a linear transformation
                            1. Image of a linear transformation
                              1. Computing kernel and image
                                1. Rank and nullity of transformations
                                  1. Fundamental theorem of linear transformations
                                  2. Matrix Representation
                                    1. Standard matrix of a linear transformation
                                      1. Finding matrix representations
                                        1. Matrix-vector multiplication as transformation
                                          1. Change of basis for transformations
                                            1. Matrix similarity
                                            2. Special Types of Linear Transformations
                                              1. One-to-one transformations
                                                1. Onto transformations
                                                  1. Isomorphisms
                                                    1. Invertible transformations
                                                      1. Isomorphic vector spaces

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                                                    4. Vector Spaces and Subspaces

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                                                    6. Inner Products and Orthogonality