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Hat


The hat is a caret-shaped symbol commonly placed on top of variables to give them special meaning. The symbol x^^ is voiced "x-hat" (or sometimes as "x-roof") in mathematics, but is more commonly known as the circumflex in linguistics (Bringhurst 1997, p. 274).

Uses of the hat in mathematics include:

1. To denote a unit vector (e.g., v^^) or an estimator (e.g., x^^).

2. To denote an estimator, e.g., mu^^=m for the sample mean.

3. As the growth rate of x in hat calculus, e.g., x^^=dlnx=dx/x (Jones 1965, who however used the symbol * instead of a hat).


See also

Bar, Caret, Estimator, Hat Polykite, Macron, Unit Vector

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References

Bringhurst, R. The Elements of Typographic Style, 2nd ed. Point Roberts, WA: Hartley and Marks, 1997.Jones, R. W. "The Structure of Simple General Equilibrium Models." J. Pol. Econ. 73, 557-572, 1965.

Referenced on Wolfram|Alpha

Hat

Cite this as:

Weisstein, Eric W. "Hat." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Hat.html

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