- True, the kernel of a linear transformation, T, from a vector space V to a vector space W is the set of all u in V such that T(u)=0.
- Thus, the kernel of a matrix transformation T(x)=Ax is the null space of A. The range of a linear transformation is a vector space.
What is the kernel of a linear transformation?
The kernel (or null space) of a linear transformation is the subset of the domain that is transformed into the zero vector.
Is kernel the same as null space?
In mathematics, the kernel of a linear map, also known as the null space or null space, is the linear subspace of the domain of the map which is mapped to the zero vector.
Is kernel the same as basis?
- The kernel of a transformation is a vector space (indeed, a subspace of the vector space on which the transformation acts).
- A basis for the kernel is never a vector space, for a basis cannot contain the zero vector.
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