The space of all functions that can be represented by a Fourier series form a vector space ( technically speaking, we call functions that have the same Fourier series expansion the " same " function, since two different discontinuous functions might have the same Fourier series ).
22.
The wheel lifting is more sudden than that of other cars, because it is caused by coming to the end of the suspension travel while there is still load on the tyre, so the load on the other ( outside ) rear wheel is a discontinuous function of cornering load, rather than just changing slope.
23.
In the other direction, the discontinuous function that rounds every tuple of real numbers to the nearest integer tuple is also a quasi-isometry : each point is taken by this map to a point within distance \ sqrt { n / 4 } of it, so rounding changes the distance between pairs of points by adding or subtracting at most 2 \ sqrt { n / 4 }.
24.
However, I couldn't find any such matrix which has no cube root : does there exist then a continuous'cube root'function which extends to the whole of M _ n ? ( I presume that every matrix does have a cube root, and so a discontinuous function would be fairly trivial by defining it pointwise, right ? ) My intuition tells me that no such function should exist-but how would I go about proving it?
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