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Concepts9

Groups

📐Linear Algebra15📈Calculus & Differentiation10🎯Optimization14🎲Probability Theory12📊Statistics for ML9📡Information Theory10🔺Convex Optimization7🔢Numerical Methods6🕸Graph Theory for Deep Learning6🔵Topology for ML5🌐Differential Geometry6∞Measure Theory & Functional Analysis6🎰Random Matrix Theory5🌊Fourier Analysis & Signal Processing9🎰Sampling & Monte Carlo Methods10🧠Deep Learning Theory12🛡️Regularization Theory11👁️Attention & Transformer Theory10🎨Generative Model Theory11🔮Representation Learning10🎮Reinforcement Learning Mathematics9🔄Variational Methods8📉Loss Functions & Objectives10⏱️Sequence & Temporal Models8💎Geometric Deep Learning8

Category

🔷All∑Math⚙️Algo🗂️DS📚Theory

Level

AllBeginnerIntermediate
∑MathIntermediate

Kronecker Product & Vec Operator

The Kronecker product A ⊗ B expands a small matrix into a larger block matrix by multiplying every entry of A with the whole matrix B.

#kronecker product#vec operator#block matrix+12
∑MathIntermediate

Orthogonal & Unitary Matrices

Orthogonal (real) and unitary (complex) matrices are length- and angle-preserving transformations, like perfect rotations and reflections.

#orthogonal matrix
Advanced
Filtering by:
#eigenvalues
#unitary matrix
#conjugate transpose
+12
∑MathIntermediate

State Space Models (SSM)

A State Space Model (SSM) describes a dynamical system using a state vector x(t) that evolves via a first-order matrix differential equation and produces outputs y(t).

#state space#matrix exponential#controllability+12
📚TheoryAdvanced

Spectral Analysis of Neural Networks

Spectral analysis studies the distribution of eigenvalues and singular values of neural network weight matrices during training.

#spectral analysis#eigenvalues#singular values+12
∑MathIntermediate

Graph Laplacian

The graph Laplacian translates a graph’s connectivity into a matrix that measures how much a function varies across edges.

#graph laplacian#laplacian matrix#normalized laplacian+11
∑MathIntermediate

Hessian Matrix

The Hessian matrix collects all second-order partial derivatives of a scalar function and measures local curvature.

#hessian matrix#second derivatives#curvature+11
∑MathIntermediate

Positive Definite Matrices

A real symmetric matrix A is positive definite if and only if x^T A x > 0 for every nonzero vector x, and positive semidefinite if x^T A x ≥ 0.

#positive definite#positive semidefinite#cholesky decomposition+11
📚TheoryIntermediate

Spectral Graph Theory

Spectral graph theory studies graphs by looking at eigenvalues and eigenvectors of matrices like the adjacency matrix A and Laplacians L and L_norm.

#spectral graph theory#laplacian#normalized laplacian+12
∑MathIntermediate

Determinant

The determinant of a square matrix measures how a linear transformation scales volume and whether it flips orientation.

#determinant#gaussian elimination#lu decomposition+12