Talk:Sherman-Morrison formula

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Where does the name come from? --RainerBlome 23:54, 27 August 2005 (UTC)

Good question. The article should begin by saying
In mathematics, in particular linear algebra, the Sherman-Morrison formula [PFTV92], named after XXXXX and XXXXX, computes the inverse of ...
for suitable values of XXXXX. Michael Hardy 22:43, 28 August 2005 (UTC)

[edit] Before and after my recent edit

[edit] BEFORE:

\begin{matrix} XY &=& (A &+& uv)(A^{-1} &-& {A^{-1}uvA^{-1} \over 1 + vA^{-1}u}) \\ &=& AA^{-1} &+& uvA^{-1} &-& {AA^{-1}uvA^{-1} + uvA^{-1}uvA^{-1} \over 1 + vA^{-1}u} \\ &=& I &+& uvA^{-1} &-& {uvA^{-1} + uvA^{-1}uvA^{-1} \over 1 + vA^{-1}u} \\ &=& I &+& uvA^{-1} &-& {(1 + vA^{-1}u) uvA^{-1} \over 1 + vA^{-1}u} \\ &=& I &+& uvA^{-1} &-& uvA^{-1} \\ &=& I \end{matrix}

[edit] AFTER:

XY = (A + uv)\left( A^{-1} - {A^{-1} uv A^{-1} \over 1 + vA^{-1}u}\right)
= AA^{-1} + uvA^{-1} - {AA^{-1}uvA^{-1} + uvA^{-1}uvA^{-1} \over 1 + vA^{-1}u}
= I + uvA^{-1} - {uvA^{-1} + uvA^{-1}uvA^{-1} \over 1 + vA^{-1}u}
= I + uvA^{-1} - {(1 + vA^{-1}u) uvA^{-1} \over 1 + vA^{-1}u}
= I + uvA^{-1} - uvA^{-1}\,
= I.

Although it's nice to have the "="s nicely aligned, various other aspects of the alignment in the \matrix version (i.e. the "BEFORE" version) of this display look bad. In particular, the fractions on the left should not all get centered the way they are. Also, the lines are too close together; it makes the fractions hard to read. Finally, the right and left parentheses are not big enough in some cases. Contrast the following:

({1 \over 2})+3
\left({1 \over 2}\right)+3

(To see what makes the difference, click on "edit this page" and see what I typed here.) Michael Hardy 22:38, 28 August 2005 (UTC)

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