specifically, in differential geometry—the musical isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle T M {\displaystyle...

Albanian television channel Musical isomorphism, the canonical isomorphism between the tangent and cotangent bundles Lists of musicals Music (disambiguation)...

some authors define the divergence of a mixed tensor by using the musical isomorphism ♯: if T is a (p, q)-tensor (p for the contravariant vector and q...

duality mappings between vector fields and one-forms: these are the musical isomorphisms flat ♭ {\displaystyle \flat } and sharp ♯ {\displaystyle \sharp }...

otherwise. In analogy to how an inner product on a vector space induces an isomorphism between a vector space and its dual given by v ↦ ⟨ v , ⋅ ⟩ {\displaystyle...

gives a natural isomorphism from the tangent bundle to the cotangent bundle, sometimes called the musical isomorphism. This isomorphism is obtained by...

vector field associated to the differential 1-form df using the musical isomorphism ♯ = ♯ g : T ∗ M → T M {\displaystyle \sharp =\sharp ^{g}\colon T^{*}M\to...

f}{\partial x^{i}}}\,\left(dx^{i}\right)^{\sharp },} where ♯ denotes the musical isomorphism ♯ : V∗ → V mentioned earlier that is induced by the inner product...

product Partial trace Interior product Raising and lowering indices Musical isomorphism Ricci calculus Let L(V, V) be the space of linear maps from V to...

metric induces a linear isomorphism between the tangent and cotangent bundles. (See Musical isomorphism). Using this isomorphism, one can define a cometric...

along a curve is the integral of the corresponding 1-form under the musical isomorphism (which takes the vector field to the corresponding covector field)...

dictionary. Just intonation § Staff notation Maneri-Sims notation Musical isomorphism, a mathematical concept which uses accidentals in its notation Stone...

space with zero curvature Flat sign, for its use in mathematics; see musical isomorphism, mapping vectors to covectors Earl "Flat" Chase (1910–1954), Canadian...

{\displaystyle V} ⁠ defines an isomorphism of V {\displaystyle V} with ⁠ V ∗ {\displaystyle V^{*}} ⁠, and so also an isomorphism of ⋀ k ( V ) {\displaystyle...

(differential) Unit tangent bundle Cotangent bundle Frame bundle Musical isomorphism Holomorphic tangent bundle The disjoint union ensures that for any...

metric gives an isomorphism between vectors and covectors), and on an oriented vector space with a nondegenerate form (an isomorphism between vectors...

^{\flat })^{-1},} where ω {\displaystyle \omega } is encoded by the musical isomorphism ω ♭ : T M → T ∗ M , v ↦ ω ( v , ⋅ ) {\displaystyle \omega ^{\flat...

inequality for Einstein manifolds Berger–Kazdan comparison theorem Musical isomorphism Parametrix Quaternion-Kähler manifold Spin(7)-manifold Symmetric...

categories of perceptual moves associated with those gestures. The concept of musical gestures has received much attention in various musicological disciplines...

to have size. (Groups are typically individuated only up to isomorphism, and isomorphism does not necessarily preserve the "sizes" assigned to group elements...

"meaningless" elements. It also discusses self-reference and formal rules, isomorphism, what it means to communicate, how knowledge can be represented and stored...

there seems to be some rough equivalence obtainable, a kind of rough isomorphism, partly global, partly local, between the brains of all the readers"...

symbols, for example E . {\displaystyle {\boldsymbol {E}}.} The musical isomorphisms will be used to indicate raising and lowering of indices with the...

antilinearity of uφ. In the real case, the antilinear isomorphism from H to its dual is actually an isomorphism, and so real Hilbert spaces are naturally isomorphic...

with piano and percussion) (1958–60), he achieved for the first time an isomorphism of the four parameters of pitch, duration, dynamics, and timbre. In 1960...

with four elements, is the smallest group that is not cyclic. Up to isomorphism, there is only one other group of order four: the cyclic group of order...

of a particular realization, or in modern language, invariant under isomorphism, as well as the classes of group with a given such property: finite groups...

group isomorphism between positive reals under multiplication and reals under addition. Logarithmic functions are the only continuous isomorphisms between...

If m = pk is a prime power with k > 1, there exists a unique (up to isomorphism) finite field G F ( m ) = F m {\displaystyle \mathrm {GF} (m)=\mathbb...

the first 32 primes 1852 = number of quantales on 5 elements, up to isomorphism 1853 = sum of primitive roots of 27-th prime, Mertens function zero 1854...