Spectral Theorem
Diagonalization of symmetric matrices. Quantum mechanics foundation.
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Similar Mathematical Theorem
Cayley-Hamilton Theorem
Matrix algebra fundamental result. Computing matrix powers.
Noether's Theorem
Symmetry implies conservation. Deep physics-mathematics connection.
Hilbert's Basis Theorem
Commutative algebra cornerstone. Ascending chain condition.
De Moivre's Theorem
Powers of complex numbers. Trigonometry and complex analysis.
Lagrange's Theorem
Fundamental group theory. Cosets and quotients.
Divergence Theorem
Gauss theorem. Connects flux and divergence.
Stokes' Theorem
Generalizes fundamental theorem of calculus. Differential forms.
Fundamental Theorem of Arithmetic
Every integer has unique prime factorization. Number theory cornerstone.
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Discover connections across different types of entities
Noether's Theorem
Time symmetry gives energy conservation. Space symmetry gives momentum conservation.
Schrödinger Equation
Fundamental equation of quantum mechanics. Predicts probability distributions.
CPT Theorem
Fundamental symmetry of nature. Antimatter and time reversal.
Black Hole Thermodynamics
Connects gravity, quantum mechanics, thermodynamics. Bekenstein-Hawking entropy.
Conservation of Energy
Most fundamental law. Energy transforms between forms but never disappears.
Snell's Law
Refraction law. n₁sin(θ₁) = n₂sin(θ₂). Explains lenses.
First Law of Thermodynamics
Conservation of energy. Energy transforms but total remains constant.
Planck's Law
Birth of quantum theory. E = hν. Black body radiation.