A linear transformation is surjective if and only if its matrix has full row rank. In other words, T : Rm → Rn is surjective if and only its matrix, which is a n × m matrix, has rank n. Note that this is possible only if n ≤ m.

How do you tell if a matrix is surjective?

If the rank equals to the amount of rows of the matrix, then it is surjective. If rank = amount of rows = amount of colums then it's bijective.

What is Surjective function in matrix?

In mathematics, a surjective function (also known as surjection, or onto function) is a function f that maps an element x to every element y; that is, for every y, there is an x such that f(x) = y. In other words, every element of the function's codomain is the image of at least one element of its domain.