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A current definition provides us this:

or·thog·o·nal   [awr-thog-uh-nl]
adjective
1.  Mathematics .
a. Also, orthographic. pertaining to or involving right angles or perpendiculars: an orthogonal projection.
b. (of a system of real functions) defined so that the integral of the product of any two different functions is zero.
c. (of a system of complex functions) defined so that the integral of the product of a function times the complex conjugate of any other function equals zero.
d. (of two vectors) having an inner product equal to zero.
e.(of a linear transformation) defined so that the length of a vector under the transformation equals the length of the original vector.
f. (of a square matrix) defined so that its product with its transpose results in the identity matrix.
2. Crystallography . referable to a rectangular set of axes.

For Software Engineering, I like to apply this term to describe how two or more  conceptual models in different perspectives will net to Zero when components of an envisioned solution are checked off or aligned with one another.

WHAT does THAT mean?

There are four essential models that can be used to describe a business solution before it is actually specified, tested, or built:

  1. Process
  2. Data
  3. Event
  4. State Transition

When conducting the project phase of Analysis where Business Requirements are intended to be fully fleshed out, these models are used to capture the ideas and expectations that the users, sponsors, management, and technical contributors disclose to the analysts.

By reviewing and comparing each of these models to the others, we can create a list that has each component in each model aligned and “Checked Off” with components in the other models.  For example: A Process and an Event item should be found to describe the same business event from their modeling perspectives.  An Event should be aligned with the appropriate data components to determine that the event can, in fact, begin with a certain condition of the data and end with another.  The evolution in a row of data in a Data Entity should align with a State Transition that reflects and depends on this data transformation.

When each of these models is used appropriately and checked off against the others, every one of modeling components should be referred to and ‘checked off’ (none remaining unchecked)!

Hence, the “Orthogonal” and mathematical proof that a set of conceptual modeling drawings and their associated supportive documentation should net to “Zero” and prove that there is only ONE (and the same) solution being described by each of these models.