Introducing

Lie group machine learning, Fanzhang, Li, and Zhao explain how to use model continuity theory to solve realistic discrete data, how to model more data with minimal data constructs, how to solve unstructured data by structured methods, how to solve nonlinear data by linear methods, how to solve the two-way mechanism of perception and cognition, and other tasks.

G be a

Lie group, H a closed subgroup of G and [GAMMA] a discrete subgroup of G.

This is our starting point: we prove in Corollary 3.3 that (*) is sufficient for the existence of a G-equivariant map S(V) [right arrow] S(W) for any compact

Lie group G.

Lie group is an effective and reliable tool to represent the states of mechanical systems in intrinsic coordinate-free approach.

In the branches of mathematics and physics,

Lie Group theory [9-11] was often used extensively.

Lie group methods are capable of handling a large number of equations.

A matrix

Lie group, which is also a differentiable manifold simultaneously, attracts more and more researchers' attention from both theoretic interest and its applications [1-5].

The general linear group is a

Lie group, whose manifold is an open subset GL(n, R) := {G [member of] [R.sup.nxm]|det G [not equal to] 0} of the linear space of all n x n nonsingular matrices.

If (1.6) is assumed to be invariant under

Lie group of infinitesimal transformations (Olver [11], Blumen and Kumei [1])