# Antonym for determinant

I am attempting to create a user interface to allow for exploring the connections between each of the variables used by a large set of equations. While examining any particular variable, I display a list of variables titled "Determinants", which contains those variables that affect the examined variable when they are changed. I am struggling to find an appropriate, preferably single-word name for the other list of variables that I'm displaying, which contains those variables that will be affected when the examined variable is changed.

For example, if `y = x + z`, then I'm referring to `x` and `z` as determinants of `y`. But what word describes `y` in relation to `x` or `z`?

• I think you might be on shaky ground calling x and z the determinants in your example. One of the 4 main subdefinitions for determinant in the full OED (specifically flagged "Mathematics") is The sum of the products of a square block or ‘matrix’ of quantities, each product containing one factor from each row and column, and having the plus or minus sign according to the arrangement of its factors in the block. Sep 19, 2018 at 16:19
• Personally, I'd just say X and Z are the inputs (or "knowns"), and Y is the output (result, value, etc.). But of course we could easily say that X = Y - Z is "the same" equation, in which case X would be the unknown result, not Y. Sep 19, 2018 at 16:23
• @FumbleFingers I agree about determinants potentially being confusing in this type of mathematical context, but in my particular case its not really likely to cause confusion because there is no matrix math going on whatsoever in the application I'm working on. Plus, that term is already being used in the same context elsewhere in the application and I've been told to use it in this instance by my boss :) thanks though! Sep 19, 2018 at 16:31
• It might make more sense to ask this on math.se, since the sought term is likely to be "domain-specific". Sep 19, 2018 at 16:48
• Some mathy versions of this are independent and dependent variables (the inputs are independent, but the dependents depend on the input). Or response variable for the output. Sep 20, 2018 at 14:31

Using 'determinant' in a math context will be very misleading because it has a primary technical meaning, especially when discussing systems of equations. If it weren't for the math context, 'determinant' would be the right word

The first likely idea, 'indeterminant', turns out not to be the opposite (or really counterpart) of 'determinant'. 'Indeterminant' means unknown, not determined, and this could actually be applied to your 'determinant' values (since even though you set them, they are initially unknown).

independent variables

and then the counterpart is the straghtforward

dependent variable.

Other terms, also from math, are 'function value', 'output', or 'response variable'.

I'm pretty sure "determinant" isn't the word you want. The word has a specific meaning in math totally unrelated to what you seem to be doing. I understand why you want to use it, because the values of x and z determine the value of y.

You know what else determines the value of y? Let's just say we look at what you have as a math function, you give two values and the function spits out another value. The function is (x + z). x and z are the "arguments" or "inputs" to the function, and y can be called the "value" or the "output" of the function.
Function (Wikipedia)

When talking about computer programming functions different terms may be used. y may be called the "result" or "return value".

Some possibilities that I've thought of so far are contingents and dependents, but I don't think either word makes it immediately obvious what the list represents.

Variables which affect other variables are called arguments of the affected variables, and variables which are affected by other variables are called functions of those other variables, so in your example y=x+z, x and z are each arguments of y, and y is a function of x and z.

You should avoid using 'determinant' because (in linear algebra) that word refers to a certain value that is meaningful only if the coefficients of the equations form a square matrix.