To each their own, but I think there is value in seeing them multiple ways. The rows can be looked at as a system of equations. The columns can be vectors to be combined. The matrix as a whole can represent the covariance of a Kalman filter or describing a confidence ellipsoid. They can be an adjacency matrix describing the edges of a graph. They can be your entire data set, and so on. Some of these uses feel more like operands than operators.