Linear Algebra
Advanced

Rank-Nullity Theorem

Relates rank and null space dimension to columns.

Formula

rank(A)+nullity(A)=n\text{rank}(A) + \text{nullity}(A) = n

Variables

nNumber of columns

Example

Fundamental theorem of linear maps

Did You Know?

The rank-nullity theorem is a conservation law: dimensions lost by a transformation reappear exactly in its null space.

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