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Matrix Calculus Foundation for Machine Learning
LI Xiucheng
SCSE Nanyang Technological University
Outline
Background
Matrix Derivative
Matrix Differentiation Rules
Machine Learning Examples
1
Notation
Wedenote
• scalars with lower-case, x;
• vectors with bold-case, x;
• matrices with upper-case, X;
• the elements of vectors or matrices with xi or Xij;
• trace as tr(X) = P Xii for X ∈ Rn×n;
i=1
• determinant as |X| for X ∈ Rn×n;
• matrices Hadamard product as X ⊙Y;
• vector or matrix inner product with h·,·i.
2
Background
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