Motivating examples. Using Julia, Jupyter, Markdown and basic latex formulas. No prior reading is needed. Intro to Julia
From [VMLS]: 1.1 Vectors, 1.2 Vector addition, 1.3 Scalar-vector Multiplication, 1.4 Inner Product, 1.5 Complexity of vector computations, 2.1 Linear Functions, 2.2 Taylor approximation, C.1.2 Scalar-valued function of a vector, C.1.3 Vector-valued function of a vector.
From [3B1B]:
Vectors, what even are they? | Essence of linear algebra, chapter 1
From [VMLS]: 3.1 Norm, 3.2 Distance, 3.3 Standard deviation, 3.4 Angle, 4.1 Clustering, 4.2 A clustering objective, 4.3 The k-means Algorithm.
From [3B1B]:
But what is a Neural Network? | Deep learning, chapter 1
Gradient descent, how neural networks learn | Deep learning, chapter 2
What is backpropagation really doing? | Deep learning, chapter 3
Backpropagation calculus | Deep learning, chapter 4
From [VMLS]: 5.1 Linear dependence, 5.2 Basis, 5.3 Orthonormal Vectors, 5.4 Gram-Schmidt Algorithm, 6.1 Matrices, 6.2 Zero and identity Matrices, 6.3 Transpose, addition and Norm, 6.4 Matrix-vector Multiplication. 7.1 Geometric transformations, 7.2 Selectors, 8.1 Linear and affine Functions, 8.2 Linear function models, 8.3 Systems of linear equations, 10.1 Matrix-matrix Multiplication, 10.2 Composition of linear Functions, 10.3 Matrix power. 10.4 QR factorization. From [3B1B]:
Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2
Linear transformations and matrices | Essence of linear algebra, chapter 3
Matrix multiplication as composition | Essence of linear algebra, chapter 4
Three-dimensional linear transformations | Essence of linear algebra, chapter 5
The determinant | Essence of linear algebra, chapter 6
From [VMLS]: 11.1 Left and right inverses, 11.2 inverse, 11.3 Solving linear equations, 11.5 Pseudo-inverse.
Inverse matrices, column space and null space | Essence of linear algebra, chapter 7
Nonsquare matrices as transformations between dimensions | Essence of linear algebra, chapter 8
Least squares approximation | Linear Algebra | Khan Academy
Abstract vector spaces | Essence of linear algebra, chapter 15