The Stakeholder Communications Matrix is very similar to the Project Communications Plan (or Matrix) used by project managers and is intended to define and document the business analyst's communication plan for the business analysis work they are about to undertake. It is one potential solution for Task 2.4 of the BABOK Guide v2.0, "Plan Business Analysis Communication".
The key difference in the use of a Stakeholder Communication Matrix as part of a business analysis plan is in the types of communications activities that occur and the outputs that are communicated.
A Project Communications Matrix will focus on project communications such as:
However, the Stakeholder Communications Matrix for a business analysis effort will focus on communications such as:
As you can see, the two efforts are very similar and complementary. They just have different focuses on what is being communicated.
The need for a communications plan is pretty well established within the project management community (if not always followed), but most Business Analysts don't think of establishing a communications plan for the business analysis effort. But in reality, creating a communications plan should be part of a business analysis planning effort. This is especially true if you are working on a process improvement effort, enterprise analysis effort, benchmarking effort, or similar BA work stream that is frequently done outside the constraints of a standard project structure.
By ensuring that you have not only identified which stakeholders will participate in different communications tasks, but also which stakeholders need to informed of the outputs of the business analysis effort, the BA ensures:
By ensuring that stakeholders have the information they need or want, the BA helps to ensure they are supportive of the analysis effort and will make the necessary time and resources available to ensure it is successful. Additionally, by keeping everyone informed throughout the process, the BA has a higher likelihood of understanding when additional time is needed for the analysis, or scope change discussions need to occur, or other unforeseen issues arise (as they always do).
A solid communication plan that is both effective and agreed to by the stakeholders is a key factor in ensuring a successful result for the analysis effort.
The Matrix usually takes the form of a table with stakeholders along the left horizontal side, and communications activities and tasks that across the top of the table. Notes and indications fill out the rest of the table indicating what stakeholders will be taking part in different communications activities, and which stakeholders need to included in different communications results.
Identify stakeholders. If you don't know your stakeholders, you don't know who you be communicating with and you can't form a business analysis plan. Make sure you don't just focus on those stakeholders who are directly affected or who need to directly participate.
Create the business analysis plan. You need to know what you want to do as part of your business analysis effort before you can plan your communications.
Create a draft communications matrix. At a minimum your matrix should include the answers to the following questions: 
Validate your plan with the stakeholders. It is imperative that you validate your proposed communication plan with the relevant stakeholders and get their buy-in. You may need to make changes based on their feedback and iterate the review process until there is agreement from all stakeholders.
Follow the plan. Having a communications plan does you no good if you don't follow it. So make sure you actually follow the plan you have laid out so that your stakeholders get the communications they expect.
Make changes as necessary. As the business analysis effort progresses, it may be necessary to modify the communications plan. Have new stakeholders been added? Has an existing stakeholder had to be replaced? Did planned dates for communication activities change? All of these are examples of when the plan documented in a stakeholder communications matrix may need to be updated.
The below image provides a simple example of a Stakeholder Communications Matrix. Note however that you can vary the information and layout. For example, rather than putting the date in the table, you could put the date as part of the communication even and track the different types of participation for different stakeholders (some might be physically present, some might virtually present and seeing a shared screen, and some might only be on the phone). The idea is to make sure the matrix has the level of detail that both you AND your stakeholders need to feel comfortable with the communications plan.