Linked from

The 12 pages that link to Kernel (linear algebra), each with the reason it gives.

• EigenvalueRelated: The eigenspace is the kernel of the transformation minus its eigenvalue times the identity.

• Rank–nullity theoremRelated: Its dimension is the part of the domain dimension lost under the map.

• Linear mapRelated: The kernel records which input directions the map collapses to zero.

• Linear operatorRelated: Its kernel reveals which inputs the operator collapses.

• Riesz representation theoremRelated: The functional's kernel is a closed subspace used in a geometric proof of representation.

• Linear functionalRelated: Its kernel is the subspace of vectors assigned scalar zero.

• Fredholm alternativeRelated: A nontrivial kernel marks the non-invertible branch and causes nonuniqueness.

• Snake lemmaRelated: Kernels of the vertical maps appear at the start of the resulting exact sequence.

• Eigenvalues and eigenvectorsRelated: For eigenvalue λ, the associated eigenvectors satisfy (A − λI)v = 0 and lie in this kernel.

• Dimension theorem for vector spacesRelated: Its dimension is the part of the domain that the theorem separates from the image.

• Fredholm theoryRelated: Its finite dimension is one part of the Fredholm index.

• Fredholm's theoremRelated: Its nonzero elements are precisely the solutions of the homogeneous equation.