Jacket matrix: Difference between revisions

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== Example 5. ==

Let <math>\mathbf {A}_0= \left[ \begin{array}{rrrr} -1 & 1 \\ 1 & -1\\ \end{array} \right],</math> and <math>\mathbf {A}_1= \left[ \begin{array}{rrrr} a-1 & -a1 \\ -1/a & -1/a\\ \end{array} \right],</math>, then the matrix <math>[\mathbf {A}]_N</math> is given by

:<math>

[\mathbf {A}]_4= \left[ \begin{array}{rrrr} -1 & 1 & a1 & -a 1\\ 1 & -1 & -1/a & -1/a \\ a-1 & -a1 & -1 & -1 \\ -1/a & -1/a & -1 & -1 \\ \end{array} \right],</math>, when N=2p and p=2.

:<math>[\mathbf {A}]_4 </math>⇒<math>

when N=2p and p=2.

\left[ \begin{array}{rrrr} U & C & A & G\\ \end{array} \right]^T\otimes\left[ \begin{array}{rrrr} U & C & A & G\\ \end{array} \right]\otimes\left[ \begin{array}{rrrr} U & C & A & G\\ \end{array} \right]^T, </math>

where ''U'', ''C'', ''A'', ''G'' denotes the amount of the DNA nucleobases and the matrix <math>[\mathbf {A}]_4 </math> is the block circulant Jacket matrix which leads to the principle of the Antagonism and Nirenberg Genetic Code matrix.

== References ==