Cofactor of an element

Another way to calculate the value of a determinant is to evaluate its cofactors. The cofactor of an element a- of the matrix is found by first deleting from the original matrix the ith row and yth column corresponding to that element the resulting array is the minor (M. ) for that element and has dimension (n - 1) X (n - 1). The cofactor is defined as... 

In general, a determinant is equal to the sum of the products of the elements in any given column (or row) with their corresponding cofactors the cofactor of an element, iit is the determinant, of next lower order, obtained by striking out the row t and the column j in which the element lies, multiplied by (—1)<+/, e.g. 

The cofactor of an element in a determinant is the minor multiplied by the appropriate factor of 1 or —1, determined as in step 3. In addition to the minor which we have defined, other minors of different order are defined, in which two or more rows and columns are deleted. We do not need to use these and will not discuss them. 

The cofactor of an element in a determinant is the minor multiplied by the appropriate factor of 1 or —1, determined as in Step 3. 

The sub-determinants, with appropriate signs, as they appear in the first stage of expansion of the determinant, are examples of cofactors. The minor, Mij of an element Oy is obtained by deleting the ith row and the jth column from the determinant, whereby the cofactor... 

The elements are numbered so that the first index tells which row, and the second index which column, the element is in. The cofactor of element an is defined as the determinant obtained by removing the row and column containing ai i. We see in (A2-2) that striking out row 1 and column 1 gives us a 3 x 3 determinant (dashed outline) as cofactor of an. Symbolize this cofactor as n I-... 

Iron is an essential cofactor of numerous enzymes, involved in, for instance, electron transfer and oxygen metabolism. It seems counterintuitive that the fourth most abundant element in the biosphere is in many instances the least bioavailable bioelement and therefore the limiting growth factor. The reason for this lies in the extremely low solubility of ferric iron (Fe3+) the prevailing form of iron under oxic conditions. Iron is precipitated as Fe(OH)3 with a solubility product of 10 39, which limits the aqueous concentration of ferric ion... 

Mecfianism of Action A trace element that is an essential component in the formation of Hgb. It s necessary for effective erythropoiesis and oxygen transport capacity of blood, and transport and utilization of oxygen, and serves as cofactor of several essential enzymes. Therapeutic Effect Replenishes body iron stores in patients who have iron deficiency anemia. 

As a cofactor is itself a determinant, we may just consider the determinant of an overlap matrix. A determinant can be expressed as a sum of products of its matrix elements. The derivative of a product of matrix elements is obtained by taking the derivative of one matrix element and multiplying this by the product of the other matrix elements. This has to be done for all the matrix elements in the product, and the results have to be added. Another way to look at a determinant is by expanding it in its first order cofactors (cf. Eq. (11)) ... 

The concentration of a co-reactant involved in a step other than the first is a cofactor in the X coefficient of that step. This coefficient appears as a factor in the numerator and as an element in some but not all matrix rows. For example, X12 is present in only the first row, X23 in only the first two rows, etc. Accordingly, the co-reactant concentration is a factor in some but not all denominator terms. As a result, the order with respect to the co-reactant is between zero and plus one. 

The coordinate—spin representation of the (N + l)-electron state al j) is a linear combination of determinants whose first column consists of elements (xr u " (k)). Subsequent columns have elements (xr a) for orbitals I a) occupied in the corresponding configuration. Rows are characterised by x r = 0,N. It is written in the notation of (3.141) as an expansion over products of the elements (xr u (k)) of the first column and their cofactors xr j) in the determinants comprising Ukly)-... 

To calculate the elemental composition of an ion, its mass must be determined to three or four decimal places. The accurate mass measurement was carried out on another cofactor-containing peptide sample (sample 2) isolated... 

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