# Ker(A)——矩阵kernel

k e r ( L ) = { v ⃗ ∈ V ∣ L ( v ⃗ ) = 0 } ker(L)=\{\vec{v}\in V|L(\vec{v})=0\}

L ( v 1 ⃗ ) = L ( v 2 ⃗ ) ⇔ L ( v 1 ⃗ − v 2 ⃗ ) = 0 ⃗ L(\vec{v_1})=L(\vec{v_2})\Leftrightarrow L(\vec{v_1}-\vec{v_2})=\vec{0}

i m ( L ) ≅ V / k e r ( L ) im(L)\cong V/ker(L)
【In linear algebra, the quotient of a vector space V by a subspace N is a vector space obtained by “collapsing” N to zero. The space obtained is called a quotient space and is denoted V/N (read V mod N or V by N).】

[1] https://en.wikipedia.org/wiki/Kernel_(linear_algebra)
[2] https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem
[3] https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)