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As shown in Section 3, in the high momentum limit,
the *r*- and the *r*-*z* track fittings are decoupled so that the
error matrix or its inverse corresponding to
the coordinate measurement errors has a
blockwise diagonal form:

| |
(1) |

where the component matrices are given by
| |
(2) |

and
| |
(3) |

Notice that, in this limit, the error matrix is determined completely by
the *y*-locations^{}
of the sampling points and the spatial resolutions
thereat.
If (*n*+1) sampling points are equally spaced and have common
resolutions, and , then the above equations
become

| |
(4) |

and
| |
(5) |

where we have defined the lever arm length *L* by
| |
(6) |

Notice that in the above equations, we have shown only upper triangles of
the matrices, since they are all symmetric.
By matrix inversions, we thus obtain
| |
(7) |

and
| |
(8) |

The above error matrices are defined with the pivotal
point (*x*_{0},*y*_{0},*z*_{0}) chosen to be at the -th hit.
From the above formulae, we can estimate, for instance,
the transverse momentum resolution or as

| |
(9) |

where the last line is none other thatn the familiar
text book expression
for the momentum resolution valid in the large *n* limit.

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*Keisuke Fujii*

*12/4/1998*