Matrix Line
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Is There A Matrix That Will Reflect Vectors Across A Line?
Suppose a line L is given through the origin in the xy plane. Is there a matrix that will reflect vectors across this line?
Yes. If the line is vertical use
-1 0
0 1
otherwise use 1/sqrt(1+m^2) times the matrix
1 m
m -1
where m is the slope of the line.
Structure of a Matrix Organization Within a Company
Before the 1970s, big corporations used to work in "silos". This denomination refers to groups of workers who functioned in separate spheres and answered to line or functional managers. You can get an idea of the process if you visualize several columns on a page. Each one is directed by a line manager, and each line manager is in charge of a single worker group. Since these groups were mostly isolated and autonomous, as a result some work functions were doubled by each silo.
Programmers of software working in an information technology organization as an example may focus to develop silo including participation with working groups to sort out problems related to customer support problems, and problems faced by finance departments. Every such task force requires a software programmer to meet the desired objectives of the working group in the organization.
The 1970s signaled an evolution in business. Organizational operations were improving at a dramatic rate in many ways. One of these was the innovation of the Matrix Organizational Structure.
Consider the information technology company discussed earlier. Note that all computer programmers are organized together into a single department and are supervised by a single manager. In this way, the manager supervises all the programming functions in an organization functioning as a single point of contact. In this type of organizational hierarchy, line managers are called functional managers because they supervise individuals who perform the same functions. This is a great example of a matrix organization.
Similarly to how the columnar organizational tables of a matrix functions, workers in this type of institution are categorized according to skills sets and are grouped into "silos." Every silo contains a single full-time manager that workers report and are accountable to. The manager is given responsibility for the promotion of workers, departmental budgeting, and the general administrative run of the silo.
By now, it may appear that matrix organizations are structured much like a traditional company, except that they categorize workers in a silo based on similar job descriptions. Another significant distinction between matrix and traditional organizations is that a matrix is also organized by rows, or lines, that go across every column.
Traditional organizations may have worked sufficiently, but they were very inefficient. Within the company many people would have the same skills. Project management situations revealed their greatest weakness, however. Instead of working directly for the project manager each team member worked under a different supervisor, in a different functional area. This was clearly the road to confusion and, ultimately, failure.
Consider, then, a matrix with several columns of workers who perform similar functions and are each supervised by a functional manager. Think of rows stretching across the column, with each row supervised by a project manager (this person can be visualized as being at the far left side of the page and leading a single row). Each row, then, intersects each column of workers. This allows each row to manifest as a group of workers that function differently and are led by one project manager.
Workers that are shared between project managers and functional managers can add to the tension that already exists. These workers have different jobs to perform which can cause conflicts of interest between the managers.
There are numerous varying types of matrix organizations, but they all have the common goal of trying to create each manager's specific functional needs with a balance of power.
About the Author
Daiv Russell is a marketing and management consultant with Envision Consulting in Tampa, Florida. Get more information on matrix organizational structure at project-management-course.info. Choose the right Project Management Software and improve your Gantt Chart Use
2009 Toyota Matrix XRS by Edmunds' Inside Line
