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Concepts140

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

AllBeginnerIntermediateAdvanced
∑MathAdvanced

Game Theory - Advanced Games

Sprague–Grundy (SG) theory solves impartial, normal-play, terminating games by assigning each position a nonnegative integer called its Grundy value.

#sprague-grundy#grundy number#nim-sum+12
∑MathIntermediate

Matrix Rank and Linear Independence

Matrix rank is the number of pivots after Gaussian elimination and equals the dimension of both the column space and the row space.

#matrix rank
89101112
#linear independence
#gaussian elimination
+12
∑MathAdvanced

Berlekamp-Massey Algorithm

Berlekamp–Massey (BM) finds the shortest linear recurrence that exactly fits a given sequence over a field (e.g., modulo a prime).

#berlekamp-massey#linear recurrence#minimal polynomial+11
∑MathAdvanced

Gaussian Elimination over GF(2)

Gaussian elimination over GF(2) is ordinary Gaussian elimination where addition and subtraction are XOR and multiplication is AND.

#gaussian elimination#gf(2)#xor basis+12
∑MathAdvanced

Linear Recurrence

A linear recurrence defines each term as a fixed linear combination of a small, fixed number of previous terms.

#linear recurrence#matrix exponentiation#kitamasa+12
∑MathIntermediate

Gaussian Elimination

Gaussian elimination is a systematic way to solve linear equations by cleaning a matrix into an upper-triangular form using row swaps, scaling, and adding multiples of rows.

#gaussian elimination#partial pivoting#row echelon form+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
∑MathIntermediate

Matrix Inverse

A matrix inverse undoes the effect of a linear transformation, just like dividing by a number undoes multiplication.

#matrix inverse#gauss-jordan#lu factorization+12