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Concepts10

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:
#determinant
#unitary matrix
#conjugate transpose
+12
∑MathIntermediate

Jacobian Matrix

The Jacobian matrix collects all first-order partial derivatives of a vector-valued function, describing how small input changes linearly affect each output component.

#jacobian matrix#partial derivatives#multivariable calculus+11
∑MathIntermediate

Systems of Linear Equations

A system of linear equations asks for numbers that make several linear relationships true at the same time, which we compactly write as Ax = b.

#systems of linear equations#gaussian elimination#row echelon form+12
∑MathIntermediate

Matrix Operations & Properties

Matrix operations like multiplication and transpose combine or reorient data tables and linear transformations in predictable ways.

#matrix multiplication#transpose#trace+12
∑MathIntermediate

Linear Diophantine Equations

A linear Diophantine equation ax + by = c has integer solutions if and only if gcd(a, b) divides c.

#linear diophantine#extended euclidean algorithm#gcd+12
⚙️AlgorithmIntermediate

Orientation and CCW

Orientation (CCW test) tells whether three points make a left turn, right turn, or are collinear by using the sign of a 2D cross product.

#orientation#ccw#cross product+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