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The "exponential map" sending a [[Lie algebra]] to the [[Lie group]] that gave rise to it shares the above properties, which explains the terminology. In fact, since '''R''' is the Lie algebra of the Lie group of all positive real numbers with multiplication, the ordinary exponential function for real arguments is a special case of the Lie algebra situation. Similarly, since the Lie algebra M(''n'', '''R''') of all square real matrices belongs to the Lie group of all invertible square matrices, the exponential function for square matrices is a special case of the Lie algebra exponential map.
See also [[exponential growth]].
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