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Strictly speaking, matrix management, which was "introduced in the 1970s in the context of competition" is the practice of managing individuals with more than one reporting line (in a matrix organization structure), but it is also commonly used to describe managing cross functional, cross business group and other forms of working that cross the traditional vertical business units – often silos – of function and geography.
What is it?
Matrix Management first started out due to an all high compound of business savvy world. This was a way to sought out talents of different individuals in different departments, in a more tactic way. So, not only do employees have more than one superior for a product or project assignments, but they can consult their peers also if need be. This is a great way to explore where employees are being more fulfilled at their greatest attributes and abilities. This may not only be a short-term project but a long term one too. If you are thinking of introducing matrix management to your team or company, first make sure it suits your employees and is the right structure for them. You want to make sure it fits their attributes and expertise. 
It is a type of organizational structure in which people with similar skills are pooled for work assignments, resulting in more than one manager (sometimes referred to as solid line and dotted line reports, in reference to traditional business organization charts).
Matrix Management is also referred to as a command – and- control status, in which some of the employees have more than one responsibility or even bosses. These particular employees have to report to one boss for that day (a project manager) so they can perform those specific duties. Then the employee will have to report to another boss at a different department for practical responsibilities. The uses and methods Matrix Management is knowing to have the best requirements for situations that vary from workloads. An example of this would be managing large collaboratives or product development tasks. 
For example, all engineers may be in one engineering department and report to an engineering manager, but these same engineers may be assigned to different projects and report to a different engineering manager or a project manager while working on that project. Therefore, each engineer may have to work under several managers to get his or her job done.
The matrix for project management
A lot of the early literature on the matrix comes from the field of cross functional project management where matrices are described as strong, medium or weak depending on the level of power of the project manager.
While some form of matrix management has become fairly common in certain industries, particularly among companies that have multiple business units and international operations, upon closer inspection, different organizations implement a matrix structure in different ways to support their needs.
Some organizations fall somewhere between the fully functional and the pure matrix. These organizations are defined in A Guide to the Project Management Body of Knowledge as ’composite’. For example, even a fundamentally functional organization may create a special project team to handle a critical project.
In popular culture
- An example of matrix-style management can be seen when Peter Gibbons messes up his TPS reports in the movie Office Space.
Matrix Management in Practice
Examples of using Matrix Management:
- Digital Equipment Corporation founder Ken Olsen spawned and popularized Matrix Management.
- ABB Group, formed from a 1988 merger and followed by "an ambitious acquisition program." Guiding this was a corporate structure whereby "local operations were organized within the framework of a two-dimensional matrix."
As for why the term is not publicly and formally affiliated with large numbers of corporations, a 2007 book about how "matrix management made a big splash in the 1970s" said that, "for the most part... companies using matrix structures tend to keep quiet about it."
In 1990 Christopher A. Bartlett and Sumantra Ghoshal writing on matrix management in the Harvard Business Review, quoted a line manager saying “The challenge is not so much to build a matrix structure as it is to create a matrix in the minds of our managers”. Despite this, most academic work has focused on structure, where most practitioners seem to struggle with the skills and behaviours needed to make matrix management a success. Most of the disadvantages are about the way people work together, not the structure.
In “Designing Matrix Organizations That Actually Work” Jay R. Galbraith says “Organization structures do not fail, but management fails at implementing them successfully.” He argues that strategy, structure, processes, rewards and people all need to be aligned in a successful matrix implementation.
In “Making the Matrix Work: How Matrix Managers Engage People and Cut through Complexity”, Kevan Hall identifies a number of specific matrix management challenges in an environment where accountability without control, and influence without authority, become the normal way of working:
- Context - matrix managers need to make sure that people understand the reasoning behind matrix working and change their behaviours accordingly
- Cooperation - a matrix is intended to improve cooperation across the silos, but it can easily lead to an increase in bureaucracy, more meetings and slower decisions where too many people are involved.
- Control - In a matrix managers are often dependent on strangers where they don't have direct control. There are many factors that can undermine trust such as cross cultural differences and communicating through technology and when trust is undermined managers often increase control. Centralization can make the matrix slow and expensive to run with high levels of escalation. Matrix managers need to directly build trust in distributed and diverse teams and to empower people, even though they may rarely get face-to-face.
- Community – the formal structure becomes less important to getting things done in a matrix so managers need to focus on the "soft structure" of networks, communities, teams and groups that need to be set up and maintained to get things done.
Paula K. Martin, in her books The Matrix Management 2.0 Body of Knowledge and Matrix Management Reinvented – The New Game in Town, introduced the concept of Matrix Management 2.0, an organizational operating System that focuses on running a matrix organization from two dimensions – the horizontal and the vertical.
MM 2.0 is defined in Matrix Management Reinvented – The New Game in Town as “A management operating system specifically designed to make a matrix organization function effectively and efficiently.” This new system updates other organizational operating systems such as Vertical Management 1.0 which is a one-dimensional, authority based system invented in the 1950s, and the Matrix Management (1.0) system that is focused on creating a specific matrix structure and authority based relationships with dual-reporting or dotted-line relationships on an Org Chart.
Matrix Management 2.0 is based on a new set of assumptions that change how we look at the organization as a system and matrix leadership.
MM 2.0 Organizational Assumptions, as defined in Matrix Management Reinvented – The New Game in Town:
- An organization is a system; therefore, the parts (areas and people) are interdependent
- The whole is equal to the product of the interaction of the parts
- Optimization of an organization is best accomplished using cooperation
- Team performance is what is important
MM 2.0 Leadership Assumptions, as defined in Matrix Management Reinvented – The New Game in Town:
- Leaders do not need authority in order to lead and be accountable
The MM 2.0 system is broken up into five SPARC Keys that cover the different aspects organizations address when they apply matrix management – Structure, Productivity, Accountability, Relationship Management and Collaborative Leadership. With MM 2.0, each Key follows the premises and principles based upon the new assumptions.
SPARC Keys, as defined in Matrix Management Reinvented – The New Game in Town:
- S Key – Horizontal & vertical structure
- P Key – Productivity of the team & organization
- A Key – Proactive and commitment-focused accountability system
- R Key – Management of non-authority horizontal relationships
- C Key – Collaborative leadership without authority
- from Japanese companies
- Marvin R. Gottlieb (2007). The Matrix Organization Reloaded: Adventures in Team and Project Management. ISBN 0275991334.
- John, Wiley. "Understanding Matrix Management". CBS Moneywatch. CBS Interactive Inc. Retrieved 8 December 2018.
- Larson, Erik, W; Gobeli, David, H. "Matrix Management: Contradictions and Insights". Sage Journal. California Management Review. Retrieved 8 December 2018.
- Tara Duggan. "Successful Organizational Structure".
- "employees report to more than one manager... combines both functional and divisional structures."
- Neff, Kristin M.; White, Ralph D. "REDEFINING PROJECT MANAGEMENT IN A MATRIX ENVIRONMENT" (PDF).
- Seet, Daniel. "Power: The Functional Manager’s Meat and Project Manager’s Poison?", PM Hut, February 6, 2009. Retrieved on March 2, 2010.
- "9 Ways Great Companies Organize Their Teams For Success". FastCompany.com.
- "early use of matrix management"Edgar H. Schein (2010). DEC Is Dead, Long Live DEC: The Lasting Legacy of Digital Equiment Corporation. ISBN 1458777677.
- gives MM components without using the term itself.Win Hindle, DEC sr. VP (2008). "Ken's Leadership".
- Glenn Rifkin. The Ultimate Entrepreneur: The Story of Ken Olsen and Digital Equipment Corporation.
- Kettinger, William J.; Marchand, Donald A. (February 2002). "Leveraging Information Locally and Globally: The Right Mix of Flexibility and Standardization" (PDF).
- Matrix management: not a structure, a frame of mind. Barlett CA, Ghoshal S, Harvard Business Review [1990, 68(4):138-145]
- Galbraith, J.R. (1971). "Matrix Organization Designs: How to combine functional and project forms". In: Business Horizons, February 1971, 29-40.
- “Making the Matrix Work: How Matrix Managers Engage People and Cut Through Complexity”, by Kevan Hall ISBN 1904838421 | ISBN 978-1904838425 |
- Martin, Paula (2013). Matrix Management 2.0™ Body of Knowledge (1 ed.). International Matrix Management Institute. p. 236. ISBN 0988334208.
- Martin, Paula (2015). Matrix Management Reinvented: Book 1 - The New Game in Town (1 ed.). International Matrix Management Institute. p. 97. ISBN 0988334216.
- Wiley, John. "Understanding Matrix Management". CBS Moneywatch. CBS Interactive Inc. Retrieved 8 December 2018.
- Cousins, Tina. "Matrix Management". Student Edition. Gale. Retrieved 11 December 2018.