Kernel

Creator
Creator
Seonglae ChoSeonglae Cho
Created
Created
2023 Apr 17 7:26
Editor
Edited
Edited
2025 Mar 24 17:14
Refs

Nullspace

This concept is entirely different from the
Kernel Method
. Here's what you need to know about kernels in linear algebra:
  • Definition: A kernel is a linear subspace of the domain of a map that gets mapped to the zero vector
  • Orthogonality Relationship: When vector v is orthogonal to vector u, we say that v belongs to the kernel of u
 
 
 
 
 
Kernel (linear algebra)
In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the linear subspace of the domain of the map which is mapped to the zero vector.[1] That is, given a linear map L : V → W between two vector spaces V and W, the kernel of L is the vector space of all elements v of V such that L(v) = 0, where 0 denotes the zero vector in W,[2] or more symbolically:
Kernel (linear algebra)
 
 

 

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