Catalog
Prerequisite Course
Matrix Algebra Foundations
Core linear algebra for ML practitioners. Covers matrix notation, arithmetic operations, geometric interpretation, determinants, matrix inversion, and eigendecomposition — the mathematical backbone of optimization, coordinate transforms, and covariance geometry in modern ML systems.
Readings
1
Notation Reference
Symbolic conventions, set notation, and Greek letter pronunciation used throughout these readings.
5 min
2
Matrices and Vectors
Matrix notation, indexing conventions, special matrix types, and vectors.
14 min
3
Matrix Operations
Transposition, addition, scalar multiplication, inner products, and matrix multiplication.
16 min
4
Vector Spaces and Geometry
Linear combinations, span, linear independence, basis, and geometric interpretation of matrices.
14 min
5
Determinants and Matrix Rank
Determinant computation, rank, null space, and the connection to invertibility.
13 min
6
Eigenvalues, Eigenvectors, and Decompositions
Eigendecomposition, spectral theorem for symmetric matrices, SVD, and applications to PCA and covariance analysis.
18 min
Quizzes
Labs
Einsum in PyTorch
Translate matrix operations to torch.einsum — unary ops, binary products, batched variants, attention, and 3DGS covariance construction.
45 min
Einsum in TensorFlow
Reproduce einsum operations in TensorFlow, build a custom Keras layer, differentiate through einsum with GradientTape, and benchmark tf.function compilation.
40 min
Practice