Kernel Extension Theorem For Vector Spaces
This application of the dimension theorem is sometimes itself called the dimension theorem. Let
- T: U → V
be a linear transformation. Then
- dim(range(T)) + dim(kernel(T)) = dim(U),
that is, the dimension of U is equal to the dimension of the transformation's range plus the dimension of the kernel. See rank-nullity theorem for a fuller discussion.
Read more about this topic: Dimension Theorem For Vector Spaces
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