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Kiran goswami Best Answer
A linear map T is called an isomorphism if the following two conditions are satisfied. T is one to one. That is, if T(x⃗ )=T(y⃗ ), then x⃗ =y⃗ T is onto. That is, if w⃗ ∈W,there exists v⃗ ∈V such that T(v⃗ )=w⃗ . See the kernel of the linear transformation. If it contains only the zero vector, then the linear transformation is one to one and hence an isomorphism .