[PDF] [PDF] 22 Properties of Linear Transformations Matrices

What are surjective injective and bijective functions?

Here is a brief overview of surjective, injective and bijective functions: Surjective: If f: P ? Q is a surjective function, for every element in Q, there is at least one element in P, that is, f (p) = q.

Is a matrix injective or surjective?

For square matrices, you have both properties at once (or neither). If it has full rank, the matrix is injective and surjective (and thus bijective)....If the matrix has full rank (rankA=min{m,n}), A is: injective if m?n=rankA, in that case dimkerA=0; surjective if n?m=rankA; bijective if m=n=rankA. What makes a matrix surjective?

Are square matrices bijective?

A matrix represents a linear transformation and the linear transformation represented by a square matrix is bijective if and only if the determinant of the matrix is non-zero. There is no such condition on the determinants of the matrices here. Are invertible matrices Injective?

What is the difference between surjective and injective?

Surjective: If f: P ? Q is a surjective function, for every element in Q, there is at least one element in P, that is, f (p) = q. Injective: If f: P ? Q is an injective function, then distinct elements of P will be mapped to distinct elements of Q, such that p=q whenever f (p) = f (q).