The Decomposition Matrix allows you to specify the relationships between the inputs and outputs of the system or subsystem you are designing. This site will then generate a draft diagram based on the Decomposition Matrix. To get started, you need indicate the approximate number of inputs and outputs on the home page of this site. On that page, you will find a form that looks something like:
In this case, a Decomposition Matrix had been defined and stored in cookies on the local machine. You have the choice of continuing to work on an existing matrix or starting a new one. We will start a new one with 8 inputs and 7 outputs. (If you have difficulty determining the number of inputs and outputs, see Design Context.) Pressing Submit will generate:
An empty matrix is displayed. Just below the matrix are choices of diagram types that can be generated based on this matrix. Below those choices are options for changing the size of the matrix. Now we can name the matrix and each of the inputs and outputs:
It is best to use meaningful terms for the inputs and outputs. This will make it easier for you to evaluate the draft diagram generated using the Decomposition Matrix. The check marks indicated that there is a relationship between a given input and a given output. For business processes, you can phrase the relationship as “the input of travel dates and locations occurs before or concurrently with the output of a flight availability request.” For data flow diagrams, you can phrase the relationship as “the input of travel dates and locations is used directly or indirectly for the output of a flight availability request.” The italicized portion of each phrase is important to remember. You can use this phrasing for each input/output combination to see if the related box should be checked. Note that you need only to look at an input/output pair and not the entire matrix. This makes it possible to have a decomposition that has many inputs and outputs. You do not need to juggle all the relationships in your head. You need only evaluate one input/output pair at a time.
This matrix is from an example decomposition described in detail in the Blog on this site. You may also want to review that.