Linear Algebra
The geometry and computation that underlies all of ML.
01Essence of Linear Algebra (1): The Essence of Vectors — More Than Just Arrows
Vectors are everywhere -- from GPS navigation to Netflix recommendations. This chapter builds your intuition from arrows …
02Essence of Linear Algebra (2): Linear Combinations and Vector Spaces
If vectors are building blocks, linear combinations are the blueprint. This chapter develops the five concepts that the …
03Essence of Linear Algebra (3): Matrices as Linear Transformations
Matrices are not tables of numbers -- they are machines that transform space. This chapter shows you how to see …
04Essence of Linear Algebra (4): The Secrets of Determinants
Determinants are not just tedious calculations -- they measure how much a transformation stretches or compresses space. …
05Essence of Linear Algebra (5): Linear Systems and Column Space
When does Ax = b have a solution? How many? The honest answer is geometric: it depends on whether b lives inside the …
06Essence of Linear Algebra (6): Eigenvalues and Eigenvectors
Some special vectors survive a matrix transformation with their direction intact -- they only get scaled. These …
07Essence of Linear Algebra (7): Orthogonality and Projections — When Vectors Mind Their Own Business
Orthogonality is what makes GPS work, noise-canceling headphones cancel, and JPEG compress. This chapter builds …
08Essence of Linear Algebra (8): Symmetric Matrices and Quadratic Forms — The Best Matrices in Town
Symmetric matrices are the 'nicest' matrices in linear algebra: real eigenvalues, orthogonal eigenvectors, and perfect …
09Essence of Linear Algebra (9): Singular Value Decomposition — The Crown Jewel of Linear Algebra
SVD decomposes any matrix -- not just square or symmetric ones. From image compression to Netflix recommendations, from …
10Essence of Linear Algebra (10): Matrix Norms and Condition Numbers — Is Your Linear System Healthy?
The condition number is a 'health report' for a linear system — it tells you whether tiny input errors will explode into …
11Essence of Linear Algebra (11): Matrix Calculus and Optimization — The Engine Behind Machine Learning
Adjusting the shower temperature is a tiny version of training a neural network: you change a parameter based on an …
12Essence of Linear Algebra (12): Sparse Matrices and Compressed Sensing — Less Is More
Sparsity is everywhere: JPEG photos, MRI scans, genomic data. Compressed sensing exploits this to recover signals from …
13Essence of Linear Algebra (13): Tensors and Multilinear Algebra
From scalars to high-dimensional data cubes -- tensors generalize vectors and matrices to arbitrary dimensions. Learn CP …
14Essence of Linear Algebra (14): Random Matrix Theory
Fill a huge matrix with random numbers, compute its eigenvalues, and watch stunning regularity emerge from chaos. Learn …
15Essence of Linear Algebra (15): Linear Algebra in Machine Learning
Machine learning speaks linear algebra as its native language. From PCA to SVMs, from matrix factorization in …
16Essence of Linear Algebra (16): Linear Algebra in Deep Learning
Deep learning is large-scale matrix computation. From backpropagation as the chain rule in matrix form, to im2col …
17Essence of Linear Algebra (17): Linear Algebra in Computer Vision
Images are matrices, geometric transformations are matrix multiplications, camera imaging is a projective map, and 3D …
18Essence of Linear Algebra (18): Frontiers and Summary
Series finale: quantum gates as unitary matrices, graph convolution as Laplacian filtering, attention as soft retrieval, …