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Mathematics
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Linear Algebra
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Rank–Nullity Theorem
Rank–Nullity Theorem
📜
The statement of the theorem
For a linear map
T
:
V
→
W
T: V \to W
T
:
V
→
W
between finite-dimensional vector spaces,
dim
(
V
)
=
rank
(
T
)
+
dim
(
ker
(
T
)
)
\dim(V) = \text{rank}(T) + \dim(\ker(T))
dim
(
V
)
=
rank
(
T
)
+
dim
(
ker
(
T
))
.
Source: Wikipedia