Siehe GeoGebra(Bauanleitung Matrizen):
\(M_k(N) \, := \, Sequence \left(Sequence \left(n + If \left(a - k < 0,a - k,k - a \right),a,1,N \right),k,1,N \right)\)
\(M_k(2)=\left(\begin{array}{rr}n&n - 1\\n - 1&n\\\end{array}\right), Det(M_k(2))=2 \; n - 1\)
\(M_k(3)=\left(\begin{array}{rrr}n&n - 1&n - 2\\n - 1&n&n - 1\\n - 2&n - 1&n\\\end{array}\right), Det(M_k(3))=4 \; n - 4\)
\(M_k(4)=\left(\begin{array}{rrrr}n&n - 1&n - 2&n - 3\\n - 1&n&n - 1&n - 2\\n - 2&n - 1&n&n - 1\\n - 3&n - 2&n - 1&n\\\end{array}\right), Det(M_k(4))=8 \; n - 12 \)
\(Det(M_k(n))=2^{n - 1} \; n - 2^{n - 2} \; \left(n - 1 \right)\)
\(Det(M_k(n))=2^{n - 2} \; \left(n + 1 \right)\)
n=5,4,3,2
\( \left\{ \left(\begin{array}{rrrrr}5&4&3&2&1\\4&5&4&3&2\\3&4&5&4&3\\2&3&4&5&4\\1&2&3&4&5\\\end{array}\right), \left(\begin{array}{rrrr}4&3&2&1\\3&4&3&2\\2&3&4&3\\1&2&3&4\\\end{array}\right), \left(\begin{array}{rrr}3&2&1\\2&3&2\\1&2&3\\\end{array}\right), \left(\begin{array}{rr}2&1\\1&2\\\end{array}\right) \right\} \)
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