What is the significance of the matrix in the LAPACK logo? This is the LAPACK linear algebra library logo:

What is the significance of this matrix?
 A: The inverse of this LAPACK logo matrix is on the back-cover of the LAPACK users' guide!
So, on the front-cover, you have the LAPACK logo matrix. You flip the book, and you inverted the matrix, and you see the inverse.
$$
\left(\begin{array}{rrrrrr}
  L &   A  &   P  &  A  &  C  &   K \\
  L &  -A  &   P  & -A  &  C  &  -K \\
  L &   A  &   P  &  A  & -C  &  -K \\
  L &  -A  &   P  & -A  & -C  &   K \\
  L &   A  &  -P  & -A  &  C  &   K \\
  L &  -A  &  -P  &  A  &  C  &  -K \\
\end{array}\right)^{-1}
=
\frac{1}{4}
\left(\begin{array}{rrrrrr}
  &    &  l &  l &  l &  l \\
  &    &  a & -a &  a & -a \\
p &  p &    &    & -p & -p \\
a & -a &    &    & -a &  a \\
c &  c & -c & -c &    &   \\
k & -k & -k &  k &    &   \\
\end{array}\right)$$
where $a=1/A$, $c=1/C$, $k=1/K$, $l=1/L$ and $p=1/P$. A space means a zero entry.
What makes this matrix special? The LAPACK logo matrix uses (1) the five LAPACK letters ( A C K L P ), and some signs, and (2) each row reads LAPACK. Then (3) the LAPACK logo matrix is invertible as long as none of A, C, K, L, and P is zero. Then (4) the inverse of this matrix can be written with the variables a=1/A, c=1/C, k=1/K, l=1/L and p=1/P only (and a 1/4 coefficient and some signs), and (5) the inverse of this matrix reads kind of lapack in column.
The idea actually came from LINPACK. The LINPACK book also had a matrix with LINPACK on it. (This time the matrix was triangular.) And the inverse of the LINPACK matrix was also on the back-cover of the LINPACK users' guide.
$$
\left(\begin{array}{rrrrrrr}
  L &   I  &  N &  P  &  A  &  C  &   K \\
    &   I  &  N &  P  &  A  &  C  &   K \\
    &      &  N &  P  &  A  &  C  &   K \\
    &      &    &  P  &  A  &  C  &   K \\
    &      &   &   &  A  &  C  &   K \\
    &      &    &   &    &  C  &   K \\
    &      &    &   &    &    &   K \\
\end{array}\right)^{-1}
=
\left(\begin{array}{rrrrrrr}
  l &  -l  &    &     &     &     &    \\
    &   i  & -i &     &     &     &    \\
    &      &  n & -n  &     &     &    \\
    &      &    &  p  & -p  &     &    \\
    &      &    &     &  a  & -a  &    \\
    &      &    &     &     &  c  & -c \\
    &      &    &     &     &     &  k \\
\end{array}\right)$$
where $a=1/A$, $c=1/C$, $i=1/I$, $k=1/K$, $l=1/L$, $n=1/N$ and $p=1/P$. A space means a zero entry.
