And who invented it? I find it totally bizarre! Where I work, it is in effect. my boss (the guy I work for) is not the man who reviews me! Review time is weird-I submit my annual report to one guy, who sends it to another guy, who does my review-and he is NOT the man I work under. As i say, i find reviews to be strange_ talkj about my performance and shortcomings, to someone who has no inkling of what I’ve been doing!
What management guru invented this-and when was it (matrix management) in vogue? 
There’s the theory and there’s the practice.
Don’t know who invented it. But the theory is that it facilitates shifting resources around from project to project. This makes more sense when you consider what matrix management replaced: project management.
With old style project management, resources were hired spefically for a project. And all the management was handled by the project.
The problem was that when the project ended, the people were either let go, or left to their own to find another project to work on. There might even be other projects in the company that were hiring, but you might not connect. There was no “cross project” planning to be able to re-use resources. Or in a crunch, to “borrow” from one project to help another.
So the theory behind matrix management is that you have two managers (and you know, the more management, the better ;-): a “line” manager, and a project manager.
Your project manager is the guy who assigns you tasks, and sees that you stay on schedule.
The line manager (or sometimes the “matrix” manager) is not concerned with your day to day work on the project. But he’s concerned with seeing how long you are assigned to your current project, and to be searching for projects that will need staffing when you will be coming free. He is to provide the “cross project” view.
The reality, sadly, is that matrix managers are usually also assigned to projects themselves (need to wear both hats), and are rarely afforded the time away from their projects to do a good job with the “line” side of things. This generally deteriorates until pretty much all the line manager ends up doing is coordinating your performance reviews.
If it provides any comfort, you are FAR from alone in being lost in the “matrix management matrix”. Take the red pill 