Mathematics for Game Development

  1. Linear Algebra: Matrices
    1. Introduction to Matrices
      1. Matrix Definition
        1. Rectangular Arrays
          1. Matrix Notation
            1. Element Indexing
            2. Matrix Dimensions
              1. Rows and Columns
                1. Square Matrices
                  1. Vector as Matrix
                  2. Matrix Types
                    1. Row Matrices
                      1. Column Matrices
                        1. Square Matrices
                          1. Rectangular Matrices
                        2. Basic Matrix Operations
                          1. Matrix Addition
                            1. Element-wise Addition
                              1. Compatibility Requirements
                              2. Matrix Subtraction
                                1. Element-wise Subtraction
                                2. Scalar Multiplication
                                  1. Scaling All Elements
                                  2. Matrix Equality
                                  3. Matrix Multiplication
                                    1. Matrix-Matrix Multiplication
                                      1. Row-Column Rule
                                        1. Dimension Compatibility
                                          1. Non-Commutativity
                                          2. Matrix-Vector Multiplication
                                            1. Transforming Vectors
                                              1. Linear Combinations
                                              2. Special Multiplication Cases
                                                1. Square Matrix Multiplication
                                                  1. Chain Multiplication
                                                2. Special Matrices
                                                  1. Identity Matrix
                                                    1. Multiplicative Identity
                                                    2. Zero Matrix
                                                      1. Additive Identity
                                                      2. Diagonal Matrix
                                                        1. Transpose Matrix
                                                          1. Symmetric Matrices
                                                          2. Inverse Matrix
                                                            1. Existence Conditions
                                                              1. Calculation Methods
                                                              2. Orthogonal Matrices
                                                                1. Rotation Matrices
                                                              3. Matrix Applications
                                                                1. Systems of Linear Equations
                                                                  1. Matrix Form
                                                                    1. Solution Methods
                                                                    2. Linear Transformations
                                                                      1. Transformation Representation
                                                                        1. Composition of Transformations

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                                                                    2. Linear Algebra: Vectors

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                                                                    4. Geometric Transformations