Subspaces have multiple meanings and appear in different fields. Mathematically, subspace refers to a part of space, and its dimension is smaller than the whole space. The so-called space refers to a set with certain properties, so subspace can be regarded as a subset. In science fiction, such as the setting in Star Trek, it is an extra continuum with special properties, which is different from the ordinary (3+ 1) dimensional space-time continuum. This setting was originally designed to avoid the speed limit in Einstein's theory of relativity.
The concept of subspace in space;
In the big space of the universe, subspace refers to many small spaces that exist together. These small spaces coexist, and there is a gap at the edge of each space. Their function is to separate each subspace, but this interval is not layered. They have their own domains like spaces, but in these domains, the rules that exist in subspaces don't work here. In this interval, the speed of light can reach more than 1 100 million times of the subspace.
Definition of subspace in linear algebra;
Let W be a subset of N-dimensional linear space V on number field F (that is, W∈V), if the elements in W satisfy
(1) If α, β∈W is arbitrary, then α+β ∈ w; (Turn off addition)
(2) If α∈W and λ∈F are arbitrary, then λ α ∈ w (logarithmic multiplication is also closed).
It is easy to prove that W also constitutes a linear space on number field F, and W is called a linear subspace of linear space V, or subspace for short.
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