├── .github └── FUNDING.yml ├── .gitignore ├── Chapters ├── 2.01 Scalars, Vectors, Matrices and Tensors │ ├── 2.1 Scalars, Vectors, Matrices, and Tensors.ipynb │ └── images │ │ ├── dimensions-transposition-matrix.png │ │ ├── matrix-addition.png │ │ ├── non-squared-matrix-transposition.png │ │ ├── scalar-vector-matrix-tensor.png │ │ ├── square-matrix-transposition.png │ │ └── vector-transposition.png ├── 2.02 Multiplying Matrices and Vectors │ ├── 2.2 Multiplying Matrices and Vectors.ipynb │ └── images │ │ ├── dot-product.png │ │ ├── plot-linear-equation.png │ │ └── system-linear-equations-matrix-form.png ├── 2.03 Identity and Inverse Matrices │ ├── 2.3 Identity and Inverse Matrices.ipynb │ └── images │ │ └── identity-matrix.png ├── 2.04 Linear Dependence and Span │ ├── 2.4 Linear Dependence and Span.ipynb │ └── images │ │ ├── intersection-2-planes-line.png │ │ ├── number-solutions-system-equations.png │ │ ├── overdetermined-system-linear-equations.png │ │ ├── python-adding-vectors-combination-1.png │ │ ├── python-adding-vectors-combination.png │ │ ├── python-one-equation.png │ │ ├── python-system-equations-with-linear-dependence.png │ │ ├── python-three-equations.png │ │ ├── python-two-equations-1.png │ │ ├── python-two-equations-no-solution.png │ │ ├── python-two-equations.png │ │ ├── python-two-vectors.png │ │ ├── representing-features.png │ │ └── underdetermined-system-linear-equations.png ├── 2.05 Norms │ ├── 2.5 Norms.ipynb │ └── images │ │ ├── l1-norm.png │ │ ├── l2-norm.png │ │ └── squared-L2-Norm.png ├── 2.06 Special Kinds of Matrices and Vectors │ ├── 2.6 Special Kinds of Matrices and Vectors.ipynb │ └── images │ │ ├── diagonal-and-symmetric-matrices.png │ │ ├── diagonal-matrix.png │ │ ├── orthogonal-matrix.png │ │ └── symmetric-matrix.png ├── 2.07 Eigendecomposition │ ├── 2.7 Eigendecomposition.ipynb │ └── images │ │ ├── output_59_0.png │ │ ├── quadratic-functions-indefinite-form.png │ │ ├── quadratic-functions-negative-definite-form.png │ │ └── quadratic-functions-positive-definite-form.png ├── 2.08 Singular Value Decomposition │ ├── 2.8 Singular Value Decomposition.ipynb │ ├── images │ │ ├── SVD_image_dim.png │ │ ├── dimensions-reconstruction-image-singular-value-decomposition.png │ │ ├── non-square-matrix-change-dimensions.png │ │ ├── output_35_7.png │ │ ├── rescaled-circle-rotated.png │ │ ├── singular-value-decomposition-understanding-dimensions.png │ │ ├── singular-value-decomposition.png │ │ ├── transformation-vector-by-matrix.png │ │ ├── unit-circle-transformation.png │ │ ├── unit-circle-transformation1.png │ │ ├── unit-circle.png │ │ └── unit-vectors-rotation.png │ └── test_svd.jpg ├── 2.09 The Moore-Penrose Pseudoinverse │ ├── 2.9 The Moore-Penrose Pseudoinverse.ipynb │ └── images │ │ ├── dataset-representation.png │ │ ├── linear-regression-r.png │ │ └── overdetermined-system-equations-python.png ├── 2.10 The Trace Operator │ ├── 2.10 The Trace Operator.ipynb │ └── images │ │ └── trace-matrix.png ├── 2.11 The Determinant │ ├── 2.11 The Determinant.ipynb │ ├── images │ │ ├── positive-negative-determinant.png │ │ ├── unit-square-area-transformed-1.png │ │ ├── unit-square-area-transformed.png │ │ └── unit-square-area.png │ └── test_svd.jpg ├── 2.12 Example - Principal Components Analysis │ ├── 2.12 Example - Principal Components Analysis.ipynb │ └── images │ │ ├── first-principal-component.png │ │ ├── gradient-descent-local-minima.png │ │ ├── gradient-descent.png │ │ ├── orthogonal-vectors.png │ │ ├── principal-component-analysis-variance-explained.png │ │ ├── principal-components-analysis-PCA-change-coordinates.png │ │ ├── principal-components-analysis-PCA-decoding-function.png │ │ ├── principal-components-analysis-PCA-encoding-function.png │ │ └── principal-components-analysis-PCA-reconstruction-function.png ├── Extra: Low-Rank Approximation │ └── Low-Rank Matrix Approximation.ipynb └── Extra: Projection │ └── Projection.ipynb ├── LICENSE ├── 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