For a linear map between finite-dimensional vector spaces, the dimension of the domain equals the rank of the map plus the dimension of its kernel (the nullity). It is a basic accounting identity underlying much of linear algebra.
Facts
StatementFor a linear map T from a finite-dimensional vector space V, rank(T) plus nullity(T) equals dim(V): the dimension of the image plus the dimension of the kernel equals the dimension of the domain. 1 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Rank-Nullity Theorem (Wikipedia)
Wikimedia Foundationlead section, matrix formulationQuote, lead section, matrix formulation
the number of columns of a matrix M is the sum of the rank of M and the nullity of M
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