Hodge star operator

Definition

In mathematics, the Hodge star operator or Hodge star is a linear map defined on the exterior algebra of a finite-dimensional oriented vector space endowed with a nondegenerate symmetric bilinear form. Applying the operator to an element of the algebra produces the Hodge dual of the element. This map was introduced by W. V. D. Hodge.

Related concepts

2-form 3D rotation group Abstract index notation Academic Press Affine connection Albert Einstein Angular momentum Antiderivation Antisymmetric tensor Atiyah–Singer theorem Augustin-Louis Cauchy Axial vector Axis of rotation Basis (linear algebra)Bernhard Riemann Binomial coefficient Bivector Canonical bundle Carl Friedrich Gauss Cartan formalism (physics)Cauchy stress tensor Charles W. Misner Chirality (physics)Christoffel symbols Closed manifold Computer vision Connection form Continuum mechanics Coordinate system Cotangent space Covariance and contravariance of vectors Covariant derivative Cross product Curl (mathematics)De Rham cohomology Degenerate bilinear form Determinant Differential form Differential geometry Dimension Dimension (vector space)Direct sum Divergence Dual space Dyadics Einstein notation Einstein tensor Electromagnetic tensor Electromagnetism Elwin Bruno Christoffel Endomorphism Engineering Eric Lengyel Euclidean geometry Euclidean space Exact form Exterior algebra Exterior calculus Exterior covariant derivative Exterior derivative Exterior form Exterior product Fiber bundle General relativity Geodesic Geometric product Glossary of tensor theory Gluon field strength tensor Gradient Gram determinant Gram matrix Gramian matrix Gregorio Ricci-Curbastro Harley Flanders Harmonic form Heat equation Hermann Grassmann Hermann Weyl Hodge decomposition Hodge theory Homotopy operator Idempotent (ring theory)Index notation Infinitesimal rotation Involution (mathematics)Isometry Isomorphism Jan Arnoldus Schouten John Archibald Wheeler Jürgen Jost Kip S. Thorne Kronecker delta Laplace operator Laplace–Beltrami operator Laplacian Leonhard Euler Levi-Civita connection Levi-Civita symbol Lie algebra Lie derivative Linear map Low-dimensional topology Manifold Mathematician Mathematics Matrix (mathematics)Matrix exponential Maxwell's equations Metric signature Metric tensor Metric tensor (general relativity)Minkowski space Mixed tensor Moment of inertia Multi-index notation Multilinear algebra Multivector Natural transformation Nonmetricity tensor Normal vector One-form Operation (mathematics)Orientation (vector space)Orthogonal complement Orthonormal basis Parity of a permutation Penrose graphical notation Physics Plücker embedding Poincare lemma Poincaré duality Projector operator Pseudo-Riemannian manifold Pseudotensor Pullback (differential geometry)Raising and lowering indices Ricci calculus Ricci curvature Riemann curvature tensor Riemannian manifold Sheaf (mathematics)Skew-symmetric matrix Sobolev space Spacetime Spin tensor Spinor Spinor-helicity formalism Springer Science+Business Media Star domain Stress–energy tensor Symmetric bilinear form Symmetric tensor Symmetrization Tensor Tensor (intrinsic definition)Tensor algebra Tensor bundle Tensor calculus Tensor contraction Tensor density Tensor field Tensor index notation Tensor operator Tensor product Tensors in curvilinear coordinates Tetrad (index notation)Topological vector space Torsion tensor Transport phenomena Transpose Transpose of a linear map Tullio Levi-Civita Twistor theory Two-point tensor Up to Van der Waerden notation Vector (mathematics and physics)Vector bundle Vector calculus Vector field Vector space Voigt notation Volume form W. V. D. Hodge Weyl equation Weyl tensor Woldemar Voigt Yang–Mills equations Élie Cartan

47 concepts already in your glossary