The kernel ker T is always a linear subspace of V. Thus, it makes sense to speak of the quotient space . The first isomorphism theorem for vector spaces states that this quotient space is naturally isomorphic to the image of T (which is a subspace of W). As a consequence, the dimension of V equals the dimension of the kernel plus the dimension of the image.
The kernel ker T is always a linear subspace of V. Thus, it makes sense to speak of the quotient space  The first isomorphism theorem for vector spaces states that this quotient space is naturally isomorphic to the image of T (which is a subspace of W). As a consequence, the dimension of V equals the dimension of the kernel plus the dimension of the image.