Definition 21.5 University Mathematics — Year 3 · অধ্যায় 21 — Differential Forms and Stokes’ Theorem The exterior product extends to a bilinear map ΛkE∗×ΛℓE∗→Λk+ℓE∗\Lambda^kE^* \times \Lambda^\ell E^* \to \Lambda^{k+\ell}E^*ΛkE∗×ΛℓE∗→Λk+ℓE∗, determined by bilinearity and (eI∗)∧(eJ∗)=eI∗∧eJ∗(e_I^*) \wedge (e_J^*) = e_I^* \wedge e_J^*(eI∗)∧(eJ∗)=eI∗∧eJ∗ (concatenate and reorder; the product is 000 if I∩J≠∅I \cap J \neq \varnothingI∩J=∅). It is associative, and graded-anticommutative: β∧α=(−1)kℓ α∧β(α∈Λk, β∈Λℓ).\beta \wedge \alpha = (-1)^{k\ell}\,\alpha \wedge \beta \qquad (\alpha \in \Lambda^k, \ \beta \in \Lambda^\ell).β∧α=(−1)kℓα∧β(α∈Λk, β∈Λℓ). প্রসঙ্গসহ পড়ো →
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