Nonsingular operators

A nonsingular operator is a mathematical function that transforms vectors in such a way that every input has a unique and well-defined output, and crucially, the inverse transformation exists. In practical terms, this means the operator doesn't distort the space into overlaps or collapse parts of it, allowing you to reverse its effects exactly. Think of it like a reversible process; if you apply the operator and then its inverse, you return to the original. Nonsingular operators are important in linear algebra because they ensure solutions to systems of equations are unique and solvable.