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Mathematics
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Linear & Multilinear Algebra
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Rank-Nullity Theorem
Rank-Nullity Theorem
Relates the dimensions of the kernel and image of a linear map.
📜
The statement of the theorem
For any linear map
f
:
V
→
W
f: V \to W
f
:
V
→
W
between finite-dimensional vector spaces,\n
dim
(
V
)
=
rank
(
f
)
+
nullity
(
f
)
\dim(V) = \text{rank}(f) + \text{nullity}(f)
dim
(
V
)
=
rank
(
f
)
+
nullity
(
f
)
Source: Wikipedia