Mathematics · University
Rank-nullity for a finite-dimensional map · formula reference
The dimension is that of the domain, not the codomain. Rank cannot exceed the domain dimension.
Formula
The dimension is that of the domain, not the codomain. Rank cannot exceed the domain dimension.
dim ker T = dim domain T − rank T
Worked example
A linear map T has domain R^15, codomain R^18, and rank 7. What is dim ker T? Round the final result to 4 decimal places if needed.
Rank-nullity in the domain gives 15 = 7 + dim ker T.
8
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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