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Say I have a vector of a matrix's singular values $[s_1, s_2, \cdots, s_N]$, and would like to define two variables, one which holds the maximum value in the vector, and another which holds an arbitrarily chosen upper limit which will be used to replace all values in the vector which exceed this limit.

Both of these variables can be considered a kind of "maximum", the first being computed from the vector, and the second being an enforced maximum.

Is there any sensible / traditional convention for naming these variables, which clearly allows one to distinguish a computed value from a chosen value? I am tempted to name the first variable $s_{max}$, but this could be an equally fitting second variable name.

Obviously it is necessary to explicitly define the variables, but I'm in search of a notation / naming convention that will make it easy to immediately distinguish computed and chosen values.

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I might use "cap" rather than "max" to briefly describe the second quantity.

Alternatively, and perhaps more conventionally, give the cap a different name like $M$.

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