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Lecture 2 Part 1: Derivatives in Higher Dimensions: Jacobians and Matrix Functions
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Classroom Contents
Matrix Calculus for Machine Learning and Beyond - IAP 2023
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- 1 Lecture 1 Part 1: Introduction and Motivation
- 2 Lecture 1 Part 2: Derivatives as Linear Operators
- 3 Lecture 2 Part 1: Derivatives in Higher Dimensions: Jacobians and Matrix Functions
- 4 Lecture 2 Part 2: Vectorization of Matrix Functions
- 5 Lecture 3 Part 1: Kronecker Products and Jacobians
- 6 Lecture 3 Part 2: Finite-Difference Approximations
- 7 Lecture 4 Part 1: Gradients and Inner Products in Other Vector Spaces
- 8 Lecture 4 Part 2: Nonlinear Root Finding, Optimization, and Adjoint Gradient Methods
- 9 Lecture 5 Part 1: Derivative of Matrix Determinant and Inverse
- 10 Lecture 5 Part 2: Forward Automatic Differentiation via Dual Numbers
- 11 Lecture 5 Part 3: Differentiation on Computational Graphs
- 12 Lecture 6 Part 1: Adjoint Differentiation of ODE Solutions
- 13 Lecture 6 Part 2: Calculus of Variations and Gradients of Functionals
- 14 Lecture 7 Part 1: Derivatives of Random Functions
- 15 Lecture 7 Part 2: Second Derivatives, Bilinear Forms, and Hessian Matrices
- 16 Lecture 8 Part 1: Derivatives of Eigenproblems
- 17 Lecture 8 Part 2: Automatic Differentiation on Computational Graphs
