In this thesis we describe in detail a generic matrix manipulator system that performs operations on matrices in a flexible way, using a graphical user interface. A user defines allowable data entries called a coefficient set, as well as closed n-ary operations based on the coefficient set, called coefficient operators. Together the coefficient set and the coefficient operators form a basis. The defined coefficient operators can then further define operations on matrices. A basis and n-ary matrix operations can be entered into the system by various ways including predefined, Java data types, JavaScript, and various XML formats defining certain mathematical structures. This described system functions similar to the RelView system, while offering additional features. These features are designed to increase convenience and usability for a user by providing support for arbitrary coefficient set types, cross platform capability, and automatic type checking for user defined expressions.