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Null Space ○꠹｜Definition｜1st｜20251119205401-00-⌔

Kernel (linear algebra) - Wikipedia

Kernel (linear algebra)

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In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain.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:

$\ker (L)=\left\{\mathbf{v}\in V\mid L(\mathbf{v})=0\right\}=L^{-1}(0).$

Printed 2026-06-28.

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Footnotes

1. Weisstein, Eric W. “Kernel”. mathworld.wolfram.com. Retrieved 2019-12-09. ↩

2. “Kernel (Nullspace) | Brilliant Math & Science Wiki”. brilliant.org. Retrieved 2019-12-09. ↩

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