Null Space

The null space of a matrix is the set of all input vectors that, when multiplied by the matrix, result in a zero vector. In simpler terms, it includes all the directions in which you can move without changing the outcome after applying the matrix transformation. This concept helps identify specific relationships or redundancies within the data or system modeled by the matrix. Understanding the null space is valuable in solving systems of equations, analyzing the behavior of linear transformations, and detecting dependencies among variables.