Concepts64
Category
Lagrangian Duality
Lagrangian duality turns a constrained minimization problem into a related maximization problem that provides lower bounds on the original objective.
Measure Theory
Measure theory generalizes length, area, and probability to very flexible spaces while keeping countable additivity intact.
Matrix Calculus
Matrix calculus extends ordinary calculus to functions whose inputs and outputs are vectors and matrices, letting you compute gradients, Jacobians, and Hessians systematically.
Singular Value Decomposition (SVD)
Singular Value Decomposition (SVD) factors any m×n matrix A into A = UΣV^{T}, where U and V are orthogonal and Σ is diagonal with nonnegative entries.
Convex Optimization
Convex optimization studies minimizing convex functions over convex sets, where every local minimum is guaranteed to be a global minimum.
Eigenvalue Decomposition
Eigenvalue decomposition rewrites a square matrix as a change of basis that reveals how it stretches and rotates space.
Optimization Theory
Optimization theory studies how to choose variables to minimize or maximize an objective while respecting constraints.
Linear Algebra Theory
Linear algebra studies vectors, linear combinations, and transformations that preserve addition and scalar multiplication.
Gradient Descent Convergence Theory
Gradient descent updates parameters by stepping opposite the gradient: x_{t+1} = x_t - \eta \nabla f(x_t).
Central Limit Theorem
The Central Limit Theorem (CLT) says that the sum or average of many independent, identically distributed variables with finite variance becomes approximately normal (Gaussian).
Probability Distributions
Probability distributions describe how random outcomes are spread across possible values and let us compute probabilities, expectations, and uncertainties.
Probability Theory
Probability theory formalizes uncertainty using a sample space, events, and a probability measure that obeys clear axioms.