Equivalence of smoothness with the basic definition for functions between vector spaces #
contMDiff_iff_contDiff
: for functions between vector spaces, manifold-smoothness is equivalent to usual smoothness.ContinuousLinearMap.contMDiff
: continuous linear maps between normed spaces are smoothsmooth_smul
: multiplication by scalars is a smooth operation
Alias of the forward direction of contMDiffWithinAt_iff_contDiffWithinAt
.
Alias of the reverse direction of contMDiffWithinAt_iff_contDiffWithinAt
.
Alias of the forward direction of contMDiffAt_iff_contDiffAt
.
Alias of the reverse direction of contMDiffAt_iff_contDiffAt
.
Alias of the forward direction of contMDiffOn_iff_contDiffOn
.
Alias of the reverse direction of contMDiffOn_iff_contDiffOn
.
Alias of the reverse direction of contMDiff_iff_contDiff
.
Alias of the forward direction of contMDiff_iff_contDiff
.
Linear maps between normed spaces are smooth #
Alias of ContinuousLinearMap.contMDiff
.
Applying a linear map to a vector is smooth within a set. Version in vector spaces. For a
version in nontrivial vector bundles, see ContMDiffWithinAt.clm_apply_of_inCoordinates
.
Applying a linear map to a vector is smooth. Version in vector spaces. For a
version in nontrivial vector bundles, see ContMDiffAt.clm_apply_of_inCoordinates
.
Smoothness of scalar multiplication #
On any vector space, multiplication by a scalar is a smooth operation.
Alias of contMDiff_smul
.
On any vector space, multiplication by a scalar is a smooth operation.
Alias of ContMDiffWithinAt.smul
.
Alias of ContMDiffAt.smul
.
Alias of ContMDiffOn.smul
.
Alias of ContMDiff.smul
.