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Bases and Dimension
Rn Matrices Tensors and the Summation Convention
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algebraic calculus Cauchy sequence coefficients complex numbers compute conserved Consider constant converges covariance curl F curve defined definition denote det(A differential equations dimensional Hilbert spaces Dirac delta function Dirac space dt dt eigenvalue eigenvectors element equations with Hamiltonian example Exercise fact finite dimensional formula Fourier series func given grad Hamilton's equations hence Hermitian adjoint Hilbert space inequality infinite integral inverse isomorphism LEMMA linear functional linear operator linear transformation linearly independent Lorentz mapping mathematical matrix multiplication Newton's equations non-zero notation Notice one-parameter orthogonal transformation orthonormal basis particle permutation perpendicular physics power series Proof properties prove quantum mechanics reader real numbers real-valued right hand side rotation satisfied scalar field skew-symmetric solution of 3.11 solve subspace Suppose symmetric THEOREM 2.1 theory unique vector field vector space vector-valued functions velocity zero