kernel

introduction

%%visits: 2 Kernel of a linear transformatio := What vectors in the domain map to the zero vector according to the transformation, {v : Av = 0}

{g ∈ G : ϕ(g) = e_g}

I feel like this is a general definition of kernels (it is) ## intuition Kernel of homomorphisms:~ anything from the range that gets mapped to the identity ## rigour Kernel of [[homomorphism]] := ker phi = {g ∈ G₁|ϕ(g) = e_G2} (where ϕ : G₁ → G₂

This kernel is a normal_subgroup, and there is a 121 relation between normal_subgroups and kernels

exam clinic

examples and non-examples

resources

tags :math:linear_algebra_1:linear_algebra_2:introduction_to_abstract_algebra:introduction_to_number_theory:

backlinks

• index_of_files.pd