Operators

Arithmetic Operators

• Addition (+)
• Subtraction (-)
• Multiplication (*)
• Division (/)
• Exponentiation (^ or **)
• Modulus (%)
• Floor Division (//)

Relational Operators

• Equality (==)
• Inequality (!=)
• Greater Than (>)
• Less Than (<)
• Greater Than or Equal To (>=)
• Less Than or Equal To (<=)

Logical Operators

• AND (&&)
• OR (||)
• NOT (!)

Set Theory Operators

• Union (∪)
• Intersection (∩)
• Complement (')
• Subset (⊆)
• Superset (⊇)
• Empty Set (∅)
• Set Difference (-)

Vector and Matrix Operators

• Dot Product (· or ⋅)
• Cross Product (× or ⨯)
• Matrix Multiplication (*)
• Transpose (T or ')
• Determinant (det)
• Inverse (⁻¹)
• Trace (Tr)
• Adjoint (adj)
• Kronecker Product (⊗)

Calculus Operators

• Derivative (d/dx or ∂/∂x)
• Integral (∫)
• Gradient (grad or ∇)
• Laplacian (∇²)
• Divergence (div)
• Curl (curl)
• Partial Differential (∂²/∂x²)
• Limit (lim)
• Taylor Series Expansion

Trigonometric Operators

• Sine (sin)
• Cosine (cos)
• Tangent (tan)
• Secant (sec)
• Cosecant (csc)
• Cotangent (cot)
• Arcsine (arcsin)
• Arccosine (arccos)
• Arctangent (arctan)
• Hyperbolic Sine (sinh)
• Hyperbolic Cosine (cosh)
• Hyperbolic Tangent (tanh)
• Inverse Hyperbolic Sine (arsinh)
• Inverse Hyperbolic Cosine (arcosh)
• Inverse Hyperbolic Tangent (artanh)

Probability and Statistics Operators

• Expected Value (E)
• Variance (Var)
• Standard Deviation (σ or SD)
• Probability (P)
• Conditional Probability (P(A|B))
• Joint Probability (P(A ∩ B))
• Marginal Probability (P(A))
• Cumulative Distribution Function (CDF)
• Probability Density Function (PDF)
• Covariance
• Correlation

Number Theory Operators

• Greatest Common Divisor (gcd)
• Least Common Multiple (lcm)
• Prime Counting Function (π)
• Euler's Totient Function (φ)
• Mobius Function (μ)

Special Functions

• Gamma Function (Γ)
• Beta Function (B)
• Riemann Zeta Function (ζ)
• Bessel Functions (J, Y, I, K)
• Legendre Polynomials (P)
• Hermite Polynomials (H)
• Laguerre Polynomials (L)

Matrix Decomposition

• Singular Value Decomposition (SVD)
• Eigenvalue Decomposition
• QR Decomposition
• Cholesky Decomposition
• LU Decomposition
• Schur Decomposition
• Jordan Normal Form

Other Mathematical Operators

• Summation (∑)
• Product (∏)
• Integral with Limits (∫ₐᵇ)
• Partial Derivative (∂)
• Infimum (inf)
• Supremum (sup)
• Absolute Value (|x|)
• Factorial (!)
• Round (round)
• Logarithm (log)
• Greatest Integer Function (⌊x⌋)
• Ceiling Function (⌈x⌉)
• Signum Function (sgn)