Linear Map

Definition

Linear Map

A linear map is a function between vector spaces over the same field that is linear:

for all , .

If , is a linear operator.

Kernel

Definition

Kernel (Algebra)

The kernel of a group morphism is the set of elements such that maps to the neutral element of :

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The neutral element is , where is the zero vector.

Rank

Let be vector spaces and be a linear map, then:

Corank

Definition

Corank

The corank of relation is the dimension of the kernel:

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