The Toyota Corrolla Matrix, which is commonly called the Toyota Matrix, is a compact hatchback produced in Canada by the Toyota Motor Corporation. The vehicle is sold in Canada, the United States, and Mexico. Toyota considers the Matrix to be a variation of the Corolla, but markets it as more of a sport styling with a hatchback.
Toyota has teamed with General Motors to produce the Matrix. The GM version is called the Pontiac Vibe, which is assembled in California. Also assembled in California was a third version of this vehicle, called the Voltz, which was sold in Japan under the Toyota name until 2004.
Identical mechanically, and nearly as much internally, the Matrix and Vibe are clothed in different sheetmetal designed by their respective brands. Both vehicles are narrow, yet tall station wagons styled in a quasi-SUV fashion (called a crossover utility vehicle or “CUV” by Toyota) and marketed to a fairly youthful market segment. This type of car is also commonly referred to as a sport wagon.
Source: Toyota manual org