请问矩阵的kernel和range是如何定义的？

看书看到这样一句话：
If T：V-> W is a linear transformation, then the set of vectors in V that T maps into 0 is called the kernel of T; it is denoted
by ker(T). The set of all vectors in W that are images under T of at least one vector in V is called the range of T; it is denoted
by R(T) .

不是很理解，如果是V和W中的向量，那为何都以映射T做标记呢，还有ker和R与矩阵的秩有何关联么？
请教各位大小牛