“cofactor”的概念、定义、翻译、参考文献-科学参考

cofactor

Mathematics

Let A be the square matrix [a_ij]. The cofactor, A_ij, of the entry a_ij is equal to (−1)^i + j times the determinant of the matrix obtained by deleting the i-th row and j-th column of A. If A is the 3×3 matrix shown, the factor (−1)^i + j has the effect of introducing a + or-sign according to the pattern on the right:

$A = [\begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix}] [\begin{matrix} + & - & + \\ - & + & - \\ + & - & + \end{matrix}] .$

So, for example,

$A_{12} = - | \begin{matrix} a_{21} & a_{23} \\ a_{31} & a_{33} \end{matrix} |, A_{31} = + | \begin{matrix} a_{12} & a_{13} \\ a_{22} & a_{23} \end{matrix} | .$

See adjoint (of a matrix)

Statistics

See matrix.

Chemistry

A nonprotein component essential for the normal catalytic activity of an enzyme. Cofactors may be organic molecules (coenzymes) or inorganic ions. They may activate the enzyme by altering its shape or they may actually participate in the chemical reaction.

Biology

A nonprotein component essential for the normal catalytic activity of an enzyme. Cofactors may be organic molecules (coenzymes) or inorganic ions. They may activate the enzyme by altering its shape or they may actually participate in the chemical reaction.

单词	cofactor
释义	cofactor Mathematics Let A be the square matrix [a_ij]. The cofactor, A_ij, of the entry a_ij is equal to (−1)^i + j times the determinant of the matrix obtained by deleting the i-th row and j-th column of A. If A is the 3×3 matrix shown, the factor (−1)^i + j has the effect of introducing a + or-sign according to the pattern on the right: $A = [\begin{matrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{matrix}] [\begin{matrix} + & - & + \\ - & + & - \\ + & - & + \end{matrix}] .$ So, for example, $A_{12} = - \| \begin{matrix} a_{21} & a_{23} \\ a_{31} & a_{33} \end{matrix} \|, A_{31} = + \| \begin{matrix} a_{12} & a_{13} \\ a_{22} & a_{23} \end{matrix} \| .$ See adjoint (of a matrix) Statistics See matrix. Chemistry A nonprotein component essential for the normal catalytic activity of an enzyme. Cofactors may be organic molecules (coenzymes) or inorganic ions. They may activate the enzyme by altering its shape or they may actually participate in the chemical reaction. Biology A nonprotein component essential for the normal catalytic activity of an enzyme. Cofactors may be organic molecules (coenzymes) or inorganic ions. They may activate the enzyme by altering its shape or they may actually participate in the chemical reaction.
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