I think that there are some types of businesses that would not benefit from a matrix organization, or at least would suffer if it was not made entirely clear. When I was first working at jobs in high school, I had a problem at a restaurant where I worked. While we had a store manager, we also had several shift managers who tried to take a more hands-on approach with servers and other crew if we had problems. I was suffering from a lack of training about some things, and the problem I had was that the shift manager who had said she was determined to help me ended up moving to a different location shortly after, and she had not felt required to talk to the store manager about the situation- in the end, I was reprimanded for not knowing things I had never been taught.
While matrix company organization sounds like a good idea, no matter what sort of business it is being used in, the matrix needs to be made clear.